Author Question: Joe owns a small coffee shop, and his production function is q = 3KL where q is total output in cups ... (Read 156 times)

dbose · **on:** Jul 1, 2018

Joe owns a small coffee shop, and his production function is q = 3KL where q is total output in cups per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labor).

If Joe's capital is currently fixed at K=3 machines, what is his short-run production function? A) q = 3L
B) q = 3L2
C) q = 9L
D) q = 3K2

Question 2

Consider a competitive market in which people consume at the point where their marginal rates of substitution between products X and Y are 3/5.

In this same market, producers produce where their marginal rates of transformation between X and Y are also 3/5. However, producers are producing 7 of Y and 3 of X, and consumers wish to consume 5 of Y and 5 of X per unit of time. Explain how this situation can exist. Also determine if it represents an equilibrium or not. If not an equilibrium, what will tend to happen in the market?

sylvia · **Reply #1 on:** Jul 1, 2018

Answer to Question 1

C

Answer to Question 2

Because MRS = MRT, one would expect output efficiency. However, producers are not producing quantities of X and Y that equal the quantities of X and Y that consumers wish to purchase. In this case producers are producing more of Y and less of X than consumers wish to purchase. Prices in the market will adjust such that the price of Y will fall and the price of X will rise. This means that the ratio of prices PX / PY increases, and the price line will move along the production frontier. An equilibrium results when the price ratio is PX > PX and PY < PY. More of X will be produced and less Y will be produced. At the equilibrium, producers will be producing quantities of both X and Y that just equal the quantities being taken from the market by consumers. At the new equilibrium the new MRT = MRS , and the competitive equilibrium will be efficient.