QUESTION 1 [40 marks]

a)   Draw a schematic representation of isoquants map for the following types of production with two inputs P  and Q: (i) no substitution is possible i.e. inputs P and Q are used in a fixed proportion and (ii) inputs P and Q can be perfectly substituted one for the other.

b)   Consider a perfectly competitive firm with the following short-run cost function: C(q) = 50q2  + 300q + 200, where q is the quantity of output. The price of this output isp = 500.

i.Calculate the profit-maximising quantity of output. Provide a detailed explanation for your answer.

ii.Suppose a subsidy of 100 is offered only to this firm in the industry. The firm must continue production in the short-run. What is the profit maximising level of output in the short run?

iii.How will your previous result (of ii) change in the long-run (when the firm can choose to leave the industry or to stay in the market)? What is the profit maximising level of output in the long run?

Suppose a firm, which needs precisely 3 units of labour input (L) and 0.5 units of capital (k) to produce one unit of output.  Find the algebraic expression of the production function; find firm’s expansion path and show it on the isoquants map.   c)   In  your  opinion,  is  the  theoretical  representation  of  a   rational  perfectly competitive  firm  realistic?   Explain  why   it  is  or  why   it  is  not,  and   in  which circumstances.

d)   A monopolist is operating in a market with a linear demand curve y(p)   =  45 − 3P with a constant marginal cost of 4, and there are no fixed costs. What is the monopolist’s profit-maximising output and what is the price it charges? What is its profit  at  this   price  and  output?  What   is  the  deadweight   loss?  Illustrate  the monopolist’s  profit  maximising  output,  price,  and  the  deadweight  loss,  with  a diagram.

e)   Suppose the monopolist in part (e) uses a single input,x, for which the price is px  =  3. The factor x is made into output y according to the production function y = 4x. How much of the input factor x will the monopolist choose to employ?

QUESTION 2 [30 marks]

Two friends (A and B) consume two goods (1 and 2) in a pure exchange economy. A begins with 15 units of good 1 and 12 units of good 2; B is originally endowed with 97 units of good 1 and 4 units of good 2. Both A and B have the same Cobb-

1     2

Douglas style utility functions over these goods U(x1, x2) = x 3y 3 , (where x, yare the quantities of good 1 and good 2 respectively).

a)   Draw  an  Edgeworth  Box  diagram  that  describes  this  situation.  Show  the endowment  point.  Sketch  the  indifference  curves  for  both  agents  and  explain how/where the trade is likely to occur.

b)   Showing and explaining all relevant conditions and intermediate steps, find the equilibrium price of the second good.

c)   Explain how the trading / bargaining process would change if A had TIOLI power and discuss the general (two) features of the TIOLI allocation.

1 2

d)   Suppose now that the utility function for A is as previously, U(x1, x2) = x1(3) x2(3) ,

but B discovered that they are allergic to good 2. Draw the new Edgeworth box with the indifference curves for each of the agents; show and discuss the Pareto optimal allocations.

QUESTION 3 [30 marks]

A farm is producing beetroot, B , and their processes cause air pollution, X. The pollution harms a nearby business producing apples, A. Both the beetroot farm and the apple  business  are  price-takers.  PF  = 15  is the  market  price  of  a  unite  of beetroots    and    PA   =  10      is    the    market     price    of     a    unit    of     apples. CB (b, x) = b2  + (x − 3)2 is the beetroot farm’s cost function for producing b  units of beetroot jointly with x units of air pollution. Ca (a, x) = a2  + 0.5xa  is the apple farm’s cost of producing a units of apples, given that the beetroot farm emits x  units of air pollution.

a)   How much output will the beetroot farm produce if pollution does not impose any external costs on the beetroot farm? What will its profits be? How much will the apple farm produce and what are its profits?

b)   How would the situation change if the two firms merged? Calculate the level of profit and for the level of pollution emitted overall if the firms merged. Would the result be efficient?

c)   Another way of achieving efficiency was suggested by Ronald Coase. Explain this idea by calculating the optimal level of pollution given that the apple farm has the right not to suffer any air pollution, and can trade these rights to the beetroot farm at the price Px   per unit of pollution.

d)   Suppose  two   housemates  are  trying  to  deciding  whether  to  buy  a  new houseplant. Anna has a utility function, defined over private consumption XA  and the provision of the houseplant G given by U(XA, G) = (2 + G)XA . Tom has a utility function, defined over private consumption XT  and the houseplant G, of U(XT, G) = (3 + G)XT .

i.What are the 2 defining characteristics of a public good? Give two original/realistic examples.

ii.If Anna has a total budget of 15 and Tom has a total budget of 40, what is the maximum price at which it would be Pareto optimal to buy the houseplant?

iii.If the houseplant cost 7, explain how free riding could occur.