Question

Park is always willing to give up 5 tangerines for 1 orange. The price of one orange is $1 and the price of one tangerine is $0.25. Park's spending budget for orange and tangerine is $10.

(1) Park is currently consuming 16 tangerines and 6 oranges. Give a suggestion about the direction of substitution for Park to improve his satisfaction.  Justify your suggestion using the economic meaning of the marginal rate of substitution and the market rate of substitution.

(2) To maximize his satisfaction, how many oranges and tangerines should Park purchase with $10 budget?  

(3) Give a graph in which the optimal consumption point shown. Include both the budget line and an indifference curve related to the optimal consumption. Clearly label the axes and mark the coordinates of the optimal consumption point.  

Answer 1

(1)

Let the amount of orange be denoted as x and that of tangerine is y. Then the consumer wants to substitute 5 y for one x at all times. therefore, the marginal rate of substitution is constant and equal to -5. On the other hand, the consumer can purchase one more orange (market price $1) by giving up purchasing 4 tangerines (each cost $0.25). The market rate of substitution between x and y is -4.

Therefore, at current consumption,

Then the marginal utility from $1 spent on oranges is greater than that of y. hence, the consumer will be better off buying more oranges and less y.

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(2)

The consumer has constant MRS implies that x and y are perfect substitutes. The utility function can be written as

In this case, the equilibrium occurs where the consumer buys only one good for which the marginal benefit from each dollar is greater. From the above discussion, this is the case for oranges. Then the consumer buys only oranges and no tangerines at the equilibrium.

At equilibrium, the consumer buys 10 oranges and 0 tangerines. This is denoted by point E on the figure below.

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(3)

The figure below demonstrates consumer equilibrium E, the equilibrium indifference curve U=50 as

The initial consumption point was A and the red line is the budget line given as