Question

Consider a one period economy in which the representative consumer has preferences over leisure (l) and consumption (c) described by the utility function

u(c, l) = c0.5l0.5

This consumer has 1 unit of time h to spend between leisure, l, and labor supply, Ns. The representative firm’s production function is Y = zNd where Nd is labor demand and z = 2 is total factor productivity. The government buys one unit of consumption good, meaning that, G = 1.

1. (a) Explain what an indifference curve is. Does the consumer prefer allocation c = 4 and l = 0.25 to the allocation c = 5 and l = 0.2? Explain.

2. (b) Find the Production possibility frontier (PPF) equation.

3. (c) From the firm’s maximization problem, find the consumer’s real wage and firm’s profits.

4. (d) Explain why it is possible to determine the competitive equilibrium of the present economy by obtaining the social planner’s solution?

5. (e) What are the conditions characterizing the social planner’s solution?

6. (f) Show that the competitive equilibrium of this economy is c∗ = 0.5 and l∗ = 0.25.

Answer 1

A) Indifference curve: Indifference curve are the graphs that represent various combinations of two commodities which an individual considers equally variable. It is widely used in microeconomics to analize consumer preferences, the effects of subsidies and taxes etc. A consumer is indifferent between these points.

Properties of IC:

1) Downward sloping (downward from left to right)

2) higher IC to lower IC

3) IC can't intersect

4) IC is bowed inward

Utility represents the satisfaction that consumers receive for choosing and consuming a product or service. In this case, a consumer will prefer where the more utility is derived.

u(c,l) = c+l where, u- utility

The utility function do not assign a numerical value to our preferences.They simply indicate the order and magnitude of preference.

B.) Production Possibility Frontier: It shows the opportunity cost of one good in terms of the other.

A PPF that is concave indicates increasing opportunity costs. Increasing opportunity costs means that no option is equally suitable. And if PPF is straight then it is suitable for either of two options.

D.) Competitive equilibrium is achieved when profit-maximizing producers and utility-maximizing consumers settle on a price that suits all parties. At this equilibrium, the quantity supplied by the producers is equal to the quantity demanded by the consumers.

It is helpful in making decision in large markets. In capitalist market it ensures the stability and competency. It can be used to predict the equilibrium price and total quantity in the market.