Microeconomics, IB and IBP

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1 Microeconomics, IB and IBP ORDINARY EXAM, December 007 Open book, 4 hours Question 1 Suppose the supply of low-skilled labour is given by w = LS 10 where L S is the quantity of low-skilled labour (in million of persons employed each year), and w is the wage rate (in dollars per hour). The demand for low-skilled labour is given by w = 8 L D What will be the perfect competitive market wage rate and employment level? Suppose the government sets a minimum wage of $5 per hour. How many people would then be employed and how many will be unemployed? To nd the equilibrium employment level we set demand equal to supply. First we rewrite the above demand and supply functions in terms of L D and L S and get Setting L D = L S we get, L S = 10w L D = 80 10w 10w = 80 10w ) w = 4 Substituting this into the demand or the supply function gives us the equilibrium level of employment L D = L S = 40: The following gure depicts the 1

2 above functions. w A B L supply L demand L The point where the demand for labour equals the supply gives L = 40 and w = 4: Consider now the case where the government sets a minimum wage equal to 5, i.e. the wage can not fall under 5: In that case it is easy to see from the above gure that the demand for labour is at point A, while the supply is given at point B. Given that the labour demanded is smaller than the labour supplied, it is the demand side that determines the level of employment. Setting w = 5 into the demand equaltion we get: L D = 80 10w = = 0 Thus, the rms will employ 0 workers at that minimum wage. At the same time there are L S = 10 5 = 50 wanting to work. This excess supply implies that there are 50 0 = 0 workers that there are unemployed. (In a way, the minimum wage changes the supply curve in the market. With a minimum wage at 5; the supply curve is horizontal until it hits the positive L S curve at point B: After that point, the supply curve follows the positive part. The interaction point of this new supply curve and of the demand curve is at point A:) 1. Suppose that instead of a minimum wage, the government pays employers a subsidy of $1 per hour for each employee. What is the total level of employment, the wage workers receive, and the wage rms pay?

3 If the government provides a wage-subsidy of 1$ per hour, the employers will pay a 1$ less per hour, i.e. the labour demand function will now be w 1 = 8 L D 10 ) 10w 10 = 80 L D ) L D = 90 10w This new demand function is depicted in the above gure as the thick negative line that starts at 9 (and stops at 90 - not shown in the gure). Equating this demand with original supply curve gives the equilibrium wage and employment: 10w = 90 10w ) w = 4:5 and thus L = 10 4:5 = 45 Note that while the worker receives 4:5$ per hour, the rm only pays :5$ per hour (the di erence is the 1$ subsidy that the government pays - these wages are not depicted in the above gure). (One could also get the same results by saying that the supply of labour will shift to the right - since it is a competitive market, it does not matter to what side of the market we o er the subsidy. The way to do it then is to say that w + 1 = LS 10, i.e. the workers will get 1$ more per hour.) Question Consider a monopolist that is deciding how to allocate output between two geographically separated markets. Demand for the two markets are given by the following functions: P 1 = 15 Q 1 P = 5 Q Moreover the monopolist s total cost is given by: T C = 5 + (Q 1 + Q ) price, output, pro ts, con- Determine the following variables: sumer surplus, if.1 the monopolist can price discriminate.. the monopolist can not price discriminate.

4 First of all, we nd the marginal revenue in each market. Since the demand curves are linear, we know that the marginal revenue curves have the same intersection and double the slope, i.e.. MR 1 = 15 Q 1 MR = 5 4Q Moreover, knowing the total cost function, we can determine the marginal cost for producing an extra unit: MC = :.1: When the rm can price discriminate, i.e. charge each market a di erent price, it should set MC = MR 1 and MC = MR : This will give = 15 Q 1 =) Q 1 = 6 and thus P 1 = 15 6 = 9 = 5 4Q =) Q = 5:5 and thus P = 5 5:5 = 14 Since we have found the prices and the quantities sold in each market it is easy to calculate the consumer surplus in each market. This is de ned by the triangle that is created under the demand function and above the price charged in that market. It is easy to see that the consumer surpluses can be calculated as CS 1 = CS = (15 9) 6 = 18 (5 14) 5:5 = 0:5 Total consumer surplus is then CS = 48:5: The total pro ts earned are = P 1 Q 1 + P Q (Q 1 + Q ) 5: Substituting the values of prices and quantities from above, we get: = :5 (6 + 5:5) 5 = 91:5.: When the rm can not price discriminate, i.e. charges the same price in both markets, then it treats the two markets as one. In that case what is interesting is the total demand. To nd that we rst write Q 1 = 15 P 1 P and Q = 1:5 : Given that the price in the two markets is the same P (P 1 = P = P ), we add these two demands into Q = Q 1 + Q = 7:5 Solving for P gives: P = 55 Q : 4

5 It is easy then to see that the total marginal revenue is: MR T otal = 55 To maximize pro ts the rm sets MC = MR T otal and thus = 55 4Q 4Q =) Q = 11:5 and thus P = 55 11:5 = Pro ts will then be = P Q Q 5 = 8:1 (i.e. lower than the pro ts in case.1 above). To nd the consumer surplus, we need rst to see how much output is sold in each market. From the demand functions and with P = = we get Q 1 = 4: and Q = 7:1: The consumer surplus is then CS 1 = CS = (15 =)4: = 9: (5 =)7:1 = 50:8 Thus, total CS = CS 1 + CS = 60:1 (i.e. higher that the consumer surplus in case.1 above - note that consumers in market 1 bene t from price discrimination while consumers in market are harmed from price discrimination). These results t perfectly with what is known about price discrimination: it bene ts the rm and hurts the consumers as a whole (it bene ts though the consumers with the most elastic demand). (Please note that simple calculation mistakes are not taken into account - it is the method that matters.) Question.1 Draw and explain the shape of an indi erence curve when products are (i) perfect complements and (ii) perfect substitutes. Explain what is the marginal rate of substitution (MRS) and what values it takes on the above two cases. Finally, describe the income and substitution e ects in these two cases. The gures below depict indi erence curves for substitutes (left panel) and complement goods (right panel) 5

6 X X B 1 A Y A B 1 Y Starting from the left panel, we draw the indi erence curve as a line, i.e. the two goods X and Y are substituted at a constant rate. This is only the case when the two goods are perfect substititutes, i.e. a one unit less of the one good is always substituted by, say, a one untit of the other good. In this one-to-one example, the MRS = 1: The important point is that in perfect substitutes the MRS is constant. We can not tell anything more about the value that the MRS takes - we only know that it is constant - the particular value depends on the substitution pattern, i.e. one-to-one, or one-to-two, or... etc. Given these indi erence curves and given a budget constraint, say 1, in the gure, the optimal consumption choice is at the point where the budget constraint meets the highest indi erence curve - in the gure point A, where the consumer buys zero units of good X and A units of good Y: If the price of good Y increases and the budget constraint is now given by line, the optimal bundle is now at point B, where the consumer consumes zero units of good Y and B units of good X. To separate the income from the substitution e ect, we draw a hypothetical budget constraint that has the same slope as the new budget constraint (line ) and leads to the original indi erence level. It is then easy to see that the income e ect is zero and that the substitution e ect is equal to the total price e ect (see also the discussion in the book around gure 4.11, page 116). Moving to the right panel of the above gure, we see that the situation for the perfgect complement goods is very diiferent. When goods are perfect complements their consumption pattern is quite particular. the two goods 6

7 are consumed in a xed ratio, i.e. one unit of X goes with, say, one unit of Y. No other consumption pattern can exist. This is also depicted in the L-shaped indi erence curves where the MRS takes the value of in nity at the vertical part and the value of zero in the horizontal part - no substitution takes place! Given a budget constraint (say line 1), the optimal choice is at point A: An increase of the price of good Y will shift the budget constraint say at line and will move the optimal choice at point B. To separate the income and substituion e ects we draw a hypothetical budget constraint that has the same slope as the new budget constraint and reaches the original indi erence level - in the fure line. It is then easy to see that now the substituition e ect is zero (logical, since the goods are perfect complements) and that income e ect is equal to the total price e ect. (see also the discussion in the book around gure 4.10, page 115.). Consider a consumer that has the following utility function U = X + Y; where U denotes utility/satisfaction level and X; Y are the two goods that she consumes. Assuming that the consumer has an income equal to 100 and faces prices P X = and P Y = 1, draw the indi erence map and determine the optimal consumption bundle. Given the above utility fucntion, we can write X = U draw this indi erence curve in the gure below. X 100 Y and we can 50 X=U Y Y The indi erence curves are drawn as one-to-one relationships, i.e. with a M RS = 1: The budget constraint instead is drawn more at. To see 7

8 why, we write the budget constraint 100 = X + Y and determine the M intersection points with the two axes: at axis X, P X = 100 = 50 and at axis M Y; P Y = = 100: It is clear that the opimal bundle is at point 100 of the horizontal axis, where the budget constraint meets the highest indi erence curve, i.e. the consumer consumes zero of good X and 100 units of the good Y. This is also logical, as the two goods are substitutable in a one-to-one basis and good X is more expensive that good Y: Question What methods do we use in order to measure welfare changes? Draw and explain your answers. There are methods: (i) consumer surplus, (ii) use of the equivalent or compensating variation method, and (ii) use of overall welfare comparisons that ony determine whether the consumers are better o or not. (i) is best when we have information of only the particular market of a good, e.g. the demand function - partial equlibrium (ii) is best in the case that we have information for more markets, e.g. indi erence curves - general equlibrium, typical a computable general equlibrium approach. (iii) is used when the only information that we have is about the orginal consumption bundle and the budget constraint (i.e. income and prices) (see discussion in the book at pages ). 4. What is the condition for an optimal choice of inputs (say, capital and labour) in a long-run production situation? Provide the intuition behind this condition. The optimal choice of inputs should full l the following condition MP L MP K = w r or MP L w = MP K r An intuition for this condition can be given from the latter expression. Given that MP L is the output a marginal worker produces and given that w is the wage of this worker, the above conditions says that the overall surplus of using a marginal labour inlput (output over costs) should be the same to the overall surplus of using capital (output over costs) - see the discussion in the book at page 40. One could provide details of how we reach that condition, see pages 8-9, but this is not necessary for answering the question. 8