Ans homework 7 EE 311 MEL. b) The monopsonist will maximize profit at the point where MRPL MEL, where Q

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1 ns homework 7 EE a) For this monopsonist w ME w ME 4 (4) ME 8 b) The monopsonist will maximize profit at the point where MRP ME, where Q MRP P In this example, Q 0.5, so MRP 0.5 P. Since P 32, MRP 16. Now setting MRP ME implies t this quantit of labor, w c) In a competitive labor market, w = MRP. So the competitive suppl of labor satisfies 4 = 16 or = 4, with w = 4 = 16. The deadweight loss due to monopson is equal to area in the graph below, or 0.5(16 8)(4 2) = 8. w 16 8 ME = 8 w = 4 MRP = a) The monopsonist will choose so that the marginal expenditure on labor equals the marginal revenue product of labor. Since the suppl of labor is linear, the marginal expenditure will have the same vertical intercept (zero in this case) and twice the slope of the suppl curve. Thus, ME = 4. The marginal revenue product of labor is just the market price (20) times the marginal product of labor (1); so MRP = 20. The monopsonist would hire labor so that 20 = 4; thus, = 5. The monopsonist will pa a wage rate on the suppl curve, so w = 2(5) = 10.

2 (b) The monopsonist produces 5 units of output with the 5 units of labor it hires. Revenue = 20(5) = 100. Costs are w= 10(5) = 50. So profit = revenue minus cost = = 50. B contrast, if it operated as a perfectl competitive firm, it would produce where the marginal revenue product of labor (20) equals the wage rate on the suppl curve for labor (2), with = 10. With its 10 units of labor the firm would produce 10 units of out, and receive revenue or 20(10) = 200. It would pa the wage rate = 2 = 2(10) = 20, so its cost would be w = 20(10) = 200. Its profits would be zero. This the firm increases its profit b 50 b acting as a monopsonist. 3. Since the elasticit of suppl of labor is constant, we can use the inverse elasticit rule for a monopsonist. [MRP - w]/w = 1/e,w. Each unit of labor produces 10 units of output (MP = 10), each of which can be sold at a price of 4. Thus, MRP = P(MP ) = 40. The inverse elasticit rule then becomes [40 - w]/w = 1/3. Thus, w = a) In equilibrium, the quantit supplied and the quantit demanded for both goods will be equal. This implies d s Q Q d s Q Q Substituting in the given curves implies P P 0.3P 3P P Here we have two equations and two unknowns. Solving the second equation for P ields P 1.5. Substituting into the first equation results in P P P 18.5 t these prices, Q 5.55 and Q 1.5. b) If the suppl of gasoline increases, the suppl curve for gasoline will shift to the right lowering the equilibrium price of gasoline as seen in the graph below.

3 Because gasoline is a complement good for autos, the reduction in the price of gasoline will increase the demand for autos. This will shift the demand curve to the right, increasing the equilibrium price and quantit for autos as seen in the following graph.

4 5. a & b) c) To be economicall efficient, the two consumers must have identical marginal rates of substitution at the allocation. While we are not given the MRS for each consumer, we are told that each has an identical utilit function. This implies that at an efficient allocation where the MRS for each consumer is the same, the ratio of apples to oranges must be the same. Since at the current allocation Josh has a ratio of apples to oranges equal to 5 and Mar has a ratio of 1.67, this allocation cannot be efficient. The contract curve in this case will be a straight line between the origins for each consumer. 6. a) b) To be economicall efficient, the MRS for the two consumers must be equal. t this allocation we have

5 MRS MRS R x, D x, R xr D 2x D (200) 10.5 Since MRS D > MRS R, the current allocation is not economicall efficient. c) t the current allocation Ron is willing to trade one baseball card for one Pokemon card, and David is willing to trade one baseball card for 10.5 Pokemon cards. If David gives Ron 9 Pokemon cards in exchange for one baseball card both consumers will be better off. Or, in other words, Ron thinks a baseball card is worth just one Pokemon card while David thinks it is worth 10.5 Pokemon cards. So both will be better off if Ron sells David a baseball card for anthing more than one Pokemon card and less than 10.5 Pokemon cards. 7. a) b) To satisf input efficienc we must have 1 2 MRTS MRTS, K, K 1 2 MP MP 1 2 MPK MPK Substituting in the given information implies Since the MRTS are not equal, the current allocation of inputs is not economicall efficient.

6 t the current allocation, Firm 1 can trade 2 units of labor for 1 unit of capital without changing output. B giving up one unit of labor to receive one unit of capital the firm can increase its output. t the current allocation Firm 2 can trade 2 units of capital for one unit of labor without affecting output. B giving up onl one unit of capital in exchange for one unit of labor Firm 2 can increase its output. Therefore, b reallocating one unit of capital from Firm 2 to Firm 1 and one unit of labor from Firm 1 to Firm 2, both firms can produce more output. 8. a) Because the technologies exhibit constant returns to scale, the production possibilities frontier will be a straight line with slope MRT x, MCx MC 1.00 Here is a graph of the production possibilities frontier for this econom. b) To achieve substitution efficienc we must have MRTx, MRS x,. t the current allocation this implies MCx x MC 3 t the current allocation we have (2) Since MRT < MRS, consumer utilit would go up if more resources were devoted to beer production (x) and less resources were devoted to peanut production ().