Economic Hw

1. Consider a representative individual who receives utility from units of food

(F) and gasoline (G). The individual’s utility function is U(F,G) = F G.

a. Graph the indifference curve associated with this utility function when U (F,G) =

4000. Specifically, for each of the following values of F: 20, 40, 60, 80, 100 and

200, solve for the corresponding value of G that would keep the consumer on the

U=4000 indifference curve. Plot these points and connect them with a smoothed line. Please label all axes clearly.

From given utility function, U(F,G) = FG and a given quantity of G, then we can find a value of F as shown in this following diagram;

Therefore, we can plot indifference curve as follows;

b. Explain “diminishing marginal rate of substitution.” Give an example which demonstrates that this utility function exhibits diminishing marginal rate of substitution.

Diminishing marginal rate of substitution is derived from the fact that the slope of indifferent curve explains the rate of trade-off between F and G while holding utility constant. To be more precise, diminishing refer to the term that consumer will be willing to give away fewer units for each additional units. For example, when we increased unit of food from 20 to 40, we need to sacrifice 100 units of Gasoline. Then, to increase unit of food from 40 to 60, we need to sacrifice only 100-66.67= 33.33 Unit of Gasoline. For increasing unit of food from 60 to 80, we need to give away unit of Gasoline for 16.67 (66.67-50) and so on.

c. This consumer has a weekly budget of $1000. If food costs $1 per unit, and gasoline costs $3 per unit, how much F and G will she consume to maximize utility?

From the information above, we knew that there are 2 equations related to find a maximization utility which are indifferent curve and constraint equation. Optimal point would represented maximum utility quantity and tangent point between indifference curve and constraint equation would represent that...