MID-TERM I ECON500, :00 (WHITE) October, Name: E-mail: @uiuc.edu All questions must be answered on this test form! For each question you must show your work and (or) provide a clear argument. All graphs must be accurate to get credit. Question 1 Suppose supply is linear. At a price of P =, supply Q = 500 and the price elasticity of supply is 0.. Therefore The supply function is Q S (P)=. points 1
Question Demand and supply functions are depicted below. Then at the equilibrium price The price elasticity of supply is. 5 points The price elasticity of demand is. 5 points P 0 Q 0
Question 3 The demand and supply curve for a product is given by Q D (P)=0 P and Q S (P)=0+3P. Thus, the equilibrium price and quantity are P=, Q=. points Now suppose that the government imposes a tax of Dollars on producers for each unit sold, i.e., if consumers pay P then producers receive P for the product. The new equilibrium price and quantity are P=, Q=. points The government s tax revenue is points 3
Question Consider the indifference curves depicted below. For a particular choice of prices and income, one of the goods is a Giffen good. points 1. Graph two budget lines (they must share either the vertical intercerpt or the horizontal intercept) that demonstrate that one of the goods is a Giffen good.. Clearly indicate the two optimal consumption choices in the graph. x 0
Question 5 A person s utility function is given by u(x 1, x )=min{x 1 + x, x 1 + 3x }. Prices are p 1 =, p = 1 and I=. Then the optimal consumption is x 1 =, x = (To get credit, you must draw the budget line and the indifference curve through the optimal consumption point). Now suppose the government introduces a tax of Dollars per unit on good which raises the price to p = 3. In order to be as well off after the price increase, the person would need an income subsidy of. (To get credit, draw the new budget line and indicate the Hicksean demand point.) Suppose the government pays this subsidy. Then the government s net revenue (tax revenue minus subsidy) is points x 0 5
Question Two friends A, and B live in different cities a and b. For simplicity suppose they consume only two goods, but the prices of the two goods differ. The prices of the two goods are p 1 =, p = in city A and p 1 = 5 and p = 1 in city B. Both have an income of I =. The two friends discuss their consumption habits. It turns out that A cannot afford B s consumption in city a and B could not afford A s consumption in city b. Nevertheless, it turns out that each is strictly better off where they are and would not want to change places with the other person. In the grid below, graph the budget lines, optimal consumption choices and indifference curves for A and B that are compatible with this information. points x 0
Question 7 A person s utility function is given by u(x 1, x )=x 1 + x. (a) Suppose prices are p 1 =, p = 5, and the person wants to get the least costly consumption bundle that give the same utility is (, ). Then Hicksean demand is (Note: A sketch of indifference curves and the budget line may help you answer the question). points x 1 = x = (b) Consider another consumer who has perfect substitute preferences (although the preferences may differ from those above). Prices are the same as in (a), but income may be different. The person optimal consumption is (, ). A perfect substitutes utility function that is compatible with this behavior is given by points u(x 1, x )= (c) Another individual has perfect complements preferences. The person s income is I= 500, prices are the same as in (a). The person consumes 50 units of good 1. A perfect complements utility function that is compatible with this behavior is given by points u(x 1, x )= 7
Question Solve the following optimization problem graphically. You must clearly indicate the feasible set by shading, and you must graph at least three lines, representing the objective, including the one through the solution. min x1,x x 1 + x, subject to (i) x 1 x + 0, (ii) x 1 + x, (iii) x 1 0, (iv) x 0. points The solution is x 1 = x = x 0
Question 9 Solve the following optimization problem graphically. You must clearly indicate the feasible set by shading, and you must graph at least three lines, representing the objective, including the one through the solution. max x1,x x 1 + 1x, subject to (i) x 1 x, (ii) x 1 + x 1, (iii) x 1, (iv) x, (v) x 1 0. points The solution is x 1 = x = x 0 9