1. Draw the budget constraints, indifference curves, and the income consumption curve for a good that has an income elasticity that is perfectly inelastic on horizontal axis, and another normal good on the vertical axis.

2. Can a consumer have a perfectly inelastic income elasticity for every good they con- sume? Explain.

3. Koichiro and Sylvia are starting a new high-volume Sushi restaurant, called Robo Sushi in Davis. While Koichiro plans to manage the business himself, he needs to employ some combination of workers and “sushi-bots” (sushi-making robots) to produce the sushi. He estimates his production function as

q = 10L0.5K
where q is the number of Sushi rolls, L is worker hours and K is sushi-bot hours.

Workers cost $10/hour and the amortized cost of sushi-bots is equivalent to $40/hr.

  • Koichiro wants to produce the maximum number of sushi-rolls possible while spending no more than $3,000/hr. Using the substitution method, what combination of Labor and Sushi-bots should he employ to maximize his output? How many sushi rolls can he make?
  • Suppose that a surge in lunch-time demand forces Koichiro to increase his output of Sushi quickly. He can only add worker-hours, and does not have time to add sushi-bots. What is his short-run marginal cost of sushi? Hint: think of

4. You are considering setting up a business manufacturing and selling giant foam hands (with fingers making the #1 gesture). The market for giant foam fingers is very competitive and the cost of one firm is given by C(q) = q2 − 10q + 64. All firms are identical and firms are free to enter or to exit the industry. Assume that the price for foam fingers is $10.

(b) Suppose you are already operating. If the market price for foam fingers were $10, how many would you produce to maximize your profit?

(a) What are the average cost, variable cost, and marginal cost functions for a single firm?

(c) If you had not entered this business (e.g. not spent any fixed cost), and the price were $10, would you want to enter this business?

(d) What would be the long-term price in equilibrium? (e.g. if more and more firms kept entering until the last one just breaks even on the entry decision).

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