1. (20 points) Suppose the electric bike market has the following production function:

Q = L0.5 K0.5. Explain and illustrate graphically that this market for electric bikes exhibits constant returns to scale and diminishing marginal product of labour.

2. (20 points) Suppose your firm faces the following production function: f(L, K) = 5LaK1-a. Discuss the shape of the output expansion path as the exponent "a" changes within the production function.

3. (30 points) Suppose that a market for electric bikes is comprised of 80 individual firms.

The firms all have the same cost function: C(q) = 100 + 4q2

a. What is the short-run market supply curve for this electric bike market?

b.Now, assume that the market demand for electric bikes is given by Q = 1280 - 30p. What is the equilibrium in this market (price and quantit

c. How many e-bikes will each firm produce and what is the total profit for each e-bike producer?

4. (20 points) Suppose that a monopolist has costs given by C(Q) = 20Q + 100 and faces a demand curve Q = 120 - 2p. What is the monopolist's optimal quantity and price charged for each unit? Illustrate graphically.