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1. In practice, rms often price their products by 'marking up\". a xed percentage over (average) cost. To investigate the consequences of markup pricing, consider a single rm that faces the demand Q = 90 P, for P g 90. The rm's TOTAL cost function is 0(9) = 2062- a. If the rm marks its prices up 50% over average cost, howr much would it produce? What price would it charge? And what would be its prots? b. In contrast, determine the rm's prot maximizing price and output decisions and its maximal prots. _ c. Given that the rm can make more money by behaving as in part b rather than as in part a, give one reason why it could choose a markup price. ti. In this example, would a 50% markup lead to a more or less eicient outcome than the prot maximizing ruie in part b? How you dene efciency? Explain. e. Is there a general relationship between markup pricing and market efciency when production exhibits constant returns to scale? f. Is there a general reiationship between markup pricing and market efciency under decreasing returns to scale? g. For the rm in part a, derive conditions under which an increase in average cost would increase prots. h. For a prot maximizing firm with the cost curve 0(6)) 2 aQE, is it possible that an increase in 0. (hence, marginal cost) would increase prots? Explain. . i. Is it possible that either a prot maximizing rm or a rm using markup pricing would choose not to operate in this market? 2. First, consider an economy with one consumer and two commodities, labor (L) and food (3}). Food can be produced from iabor according to the production function y = L(4 ' L). The consumer is endowed with 4 units of labor and has preferences represented by My, L) = y(4 L). a. Characterize the set of Pareto efcient allocations for this economy. b. Suppose the consumer owns the technology but it is operated independently as a prot maximising enterprise. Compute a competitive equilibrium, taking food as numeraire. Next, suppose there are two consumers, A and B, each of whom is endowed with 4 units of labor and has the utility function new\" 1.2,) = y,(4 15,), where y, and L, denote the quantities of food and labor of agent i. c. Characterize the interior Pareto eicient allocations in this case- How do they differ from each other? 6.. Is it possible that at an efcient allocation, an agent might work (L, > 0) but con- sume no food (31,: = 0)? Explain. e. Suppose that here, too, resources were allocated via the Walrasian mechanism with each consumer owning half of the rm. Prove that the equilibrium wage would be lower than in the equilibrium in part b- Explain why it is. f. Under these circumstances, could there be an asymmetric Walrasian equilibrium in which the consumers get different consumption bundles? Explain. g. Explain what is meant by the statement, \"the decreasing portion of the production function is economically irrelevau .\" h. Suppose that instead of L = L1+Lg it were the case that L = L1+0L2, for 0