Cost and perfect competition
1. If a perfectly competitive firm produces goods with the following technology: Y= min (2X1, 3X2) where X1 and X2 are the inputs and Y is the output. The unit cost of both x1 and x2 is 100. Find the minimum cost of producing 300 units of output.
2. A firm has a production function of the form Y=2L+5K where Y is the output and L and K are the two inputs. The unit cost of L is $2 and per unit cost of K is $3.
a) Draw an iso-cost line for this firm, showing combinations of L and K that cost $6 and another iso-cost line showing combinations that cost $12. What are the slopes of these iso-cost lines?
b) Sketch the production isoquant depicting 10 units of output. Find the minimum cost of producing 10 units of output.
Perfect Competition
3. Just Juice is in a perfectly competitive long run equilibrium selling juice at a price of $5 per gallon. Demand falls and the price falls to $3 per gallon. At this new price, Just Juice produces 100 gallons of juice at an average variable cost (AVC) of $3 per gallon. Will Just Juice continue to produce in the short run? What if AVC at 100 gallons of production was $3.25 per gallon? Explain your reasoning using a graph (s).
Monopoly
4. AC Inc. has a monopoly in the market for little green houses. AC's total cost function is 10,000+ 0.10y2 and it faces the inverse demand curve P=44-y.
a) What are the expressions for AC's total revenue, marginal revenue, total cost and marginal cost as a function of output? What is AC's fixed cost and what is the variable cost?
b) What is the expression for AC's profits as a function of output?
c) What level of output will AC choose in order to maximize its profits? What price will AC charge? What will its marginal revenue and marginal cost be?
d) What is the efficient level of output in the little green house industry?
e) Graph AC's demand, marginal revenue and marginal cost function. Indicate on the graph AC's profit maximizing output and price, and the efficient output in the industry. Indicate the "deadweight loss" due to the monopoly.
Game Theory
5. Find dominant strategy and Nash equilibrium in the following game:
Oligopoly
6. For Cournot dupolists that face a market demand curve of P=44-Q and a constant marginal cost of 20, find each firm's reaction function. Find the Cournot equilibrium price and quantity. If the firms colluded, what would the cooperative equilibrium quantity and price be?