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# ps5 - (Use a standard consumer’s surplus “triangle”...

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Economics 101A Problem Set Number 5 Due: Tuesday October 14 in class 1. An industry consists of two firms. Firm 1 has cost function C(y 1 ) = y 1 + y 1 ² while firm 2 has cost function C(y 2 ) = 3y 2 + ½ y 2 ² a) Suppose each firm operates as a competitive supplier. Find the two firms’ supply functions y 1 * (p) and y 2 * (p), where p is the price of output. Find the industry supply curve. Hint: draw a picture! b) Assuming the two firms operate as price takers, find the industry equilibrium when the industry demand is y = 9/2 ! ½ p. c) Suppose now that a single monopolist buys the two firms and operates them as one. Find the monopolist’s marginal cost schedule. Find the monopolist’s optimal level of output. d) Calculate an approximate expression for the “deadweight” loss of monopoly.
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Unformatted text preview: (Use a standard consumer’s surplus “triangle” calculation). 2. A consumer has a utility function u(x 1 , x 2 ) = x 1 " x 2 1 ! " . a) Find the consumers demand functions, expenditure functions, and compensated demand functions. Hint: we have done these calculations before – look up the answers from the notes and earlier problem sets . b) Suppose the consumer has initial income I=10, and faces prices p 1 = p 2 = 1. Consider the effect of a change in the price of the first good to p 1 =2. Calculate the consumers surplus (CS) associated with this change, the compensating variation (CV), and the equivalent variation (EV). Draw a graph illustrating the relation between CS, CV and EV for this case....
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