Based on the following graph,if the price of X is $7.50 per unit,how many units of X will a utility-maximizing consumer choose? The consumer's income is $600.
A)25
B)30
C)35
D)50
E)none of the above

Question

Based on the following graph,if the price of X is $7.50 per unit,how many units of X will a utility-maximizing consumer choose?  The consumer's income is $600.
A)25 
B)30 
C)35 
D)50 
E)none of the above

Quizplus · Accepted Answer

To find the utility-maximizing quantity of X, we need to find the point where the budget line (represented by the straight line with a slope of -80/60 = -4/3) is tangent to the highest possible indifference curve. This occurs at the point where the MRS (marginal rate of substitution) is equal to the price ratio.

At a price of $7.50 per unit, the consumer can purchase 80/7.5 = 10.67 units of X with their entire income. To find the exact quantity of X that maximizes utility, we need to find the quantity where the slope of the indifference curve (the marginal rate of substitution) is equal to -7.5/12 (the price ratio). From the graph, we can estimate that this occurs at a quantity of about 35 units of X. Therefore, the answer is C) 35.

Based on the Following Graph,if the Price of X Is