ECON 201 Intermediate Microeconomics Midterm Examination Suggested Solution Tuesday, April 24, 2012

Transcription

1 ECON 201 Intermediate Microeconomics Midterm Examination Suggested Solution Tuesday, April 24, 2012 Beomsoo Kim Spring (25 points) Draw a set of indifference curves for the following pairs of goods: (a) (5 points) Hamburgers and carrots for a vegetarian who neither likes nor dislikes meat. (Vegetarians do not eat meat.) Place carrot on the horizontal axis. Hamburger is neutral good for a vegetarian. The utility is only determined by the amount of carrots. (b) (5 points) Peanut butter and jelly for an individual that will not eat peanut butter sandwiches or jelly sandwiches, but loves peanut butter and jelly sandwiches made with two parts peanut butter and one part jelly. Place jelly on the horizontal axis. Peanut Butter and Jelly are compliment goods. The ratio of two goods is, Peanut Butter : Jelly = 2 : 1. Page 1 of 8

2 (c) (5 points) Tickets for Knotts Berry Farm (KBF) and Universal Studios (US) for a tourist that believes that KBF and US are perfect substitutes. Place US on the horizontal axis. When two goods are perfect substitutes, the slope of the indifference curve remains constant. (d) (10 points) Ice cream and pie if these are goods that you like, but if you consume enough of either, you get sick of them. If you are sick of a good, consuming more of it lowers your utility. Place pie on the horizontal axis. There is a point that maximizes utility, which is called a bliss point. As one gets full of ice cream and pie, a point of maximum value is reached, illustrated by a large black dot, a bliss point. It is a point at which further increases in consumption reduce utility. Page 2 of 8

3 2. (10 points) Suppose that a small market Major League Baseball team currently charges $12 for a ticket. At this price, they are able to sell 12,000 tickets to each game. If they raise ticket prices to $15, they would sell 11,053 tickets to each game. (a) (5 points) What is the price elasticity of demand at $12? The price elasticity of demand is, ( ) ( ) P Q E = Q P ( ) ( ) = = (b) (5 points) If the demand curve is linear, what is the algebraic expression for demand? If the demand curve is linear, it is in the form of QD = a + bp. Also, we know that ( ) P E = b Q ( ) Q b = E P ( ) = = 316 Rearranging the linear expression for demand allows us to solve for a as follows: a = QD bp = (12) = We may now write the linear expression for demand as QD = P. Page 3 of 8

4 3. (30 points) Lisas budget line and her satisfaction maximizing market basket, A, are shown in the diagram below. (a) (5 points) Suppose that price of AOG is $1. What is Lisa s income? $100 (b) (5 points) What is the price of Food? $5 Page 4 of 8

5 (c) (10 points) Suppose that Lisa is given $10 worth of coupons that must be spent on food. Draw Lisas new budget line with the coupons? Indicate the intercept of x axis. line : a b c (d) (5 points) Suppose that Lisa is given $50 in cash instead of $50 in coupons. How will this alter Lisas budget line? line : d b c (e) (5 points) Is Lisa indifferent between the food coupon and cash program, or does she prefer one program over the other? Draw an indifference curve to illustrate your answer. It depends on the indifference curve that she has. When the indifference curves are u 1 (coupon) u 2 (cash), she prefers the cash program to the coupons. However, if the case of u 0, there is no difference in those two programs. 4. (45 points) The firm produces tutoring services for students in economics by combining computer and tutor according to the production function: q = 5KL where q is the number of lessons, K is the number of computer and L is the number of tutors. The going rate for tutors is $100/day, while the daily cost of renting a computer is $125. K and L are the only inputs for production. (a) (5 points) What is the Marginal Physical Product of L? MP P l = 5K (b) (5 points) What is the Marginal Physical Product of K? MP P k = 5L Page 5 of 8

6 (c) (10 points) If the firm wants to produce 100 lessons per day what will be the best combination of computers and tutors? MP P l MP P k = w r K L = K = 4 5 L q = L L = 100 q = L 2 = 25 L = 5, K = 4 (d) (10 points) What is the minimum cost to produce 100 lessons? cost = = 1000 $1000 (e) (10 points) Is this production increasing returns to scale, constant returns to scale or decreasing returns to scale? Show your work. Increasing returns to scale: Q = 5(2K)(2L) = 4(5KL) > 2Q = 2(5KL) (f) (5 points) If the production function changes to q = 5K 0.5 L 0.5 what is your answer for part (e)? Constant returns to scale Page 6 of 8

7 5. (20 points) A competitive firm has the following short-run cost function : C(q) = q 3 8q q + 5 (a) (5 points) Find MC, AC, and AV C and sketch them on a graph. MC = 3q 2 16q + 30 AC = q 2 8q q AV C = q 2 8q + 30 (b) (5 points) At what range of prices will the firm supply zero output? In short-run, when price is below the AV C, the firm will supply zero output. MC = AV C : q = 4 When q = 4 then substitute to MC then P = MR = AR = MC = 14. Thus, when the price falls below 14, the firm will supply zero output. (c) (5 points) Identify the firm s supply curve on your graph. Supply Curve on the graph Until the price is up to 14, the firm will not produce. When the price is over 14, the firm s supply curve will follow the MC curve. Page 7 of 8

8 (d) (5 points) At what price would the firm supply exactly 6 units of output? MC = 3q 2 16q + 30 q = 6 MC(6) = 42 When the price is 42, the firm would supply exactly 6 units of output. Page 8 of 8