Use the table below to answer the following questions.
Table 8.2.1
-Refer to Table 8.2.1.Consider Sam's utility from sailing and skiing.The price of sailing is $10 per hour and the price of skiing is $20 per hour;Sam's income to spend on these activities is $80.In consumer equilibrium,Sam will sail for
A)3 hours and ski for 2 hours.
B)2 hours and ski for 4 hours.
C)4 hours.
D)4 hours and ski for 2 hours.
E)8 hours.

Question

Use the table below to answer the following questions.
Table 8.2.1 
-Refer to Table 8.2.1.Consider Sam's utility from sailing and skiing.The price of sailing is $10 per hour and the price of skiing is $20 per hour;Sam's income to spend on these activities is $80.In consumer equilibrium,Sam will sail for
A)3 hours and ski for 2 hours. 
B)2 hours and ski for 4 hours. 
C)4 hours. 
D)4 hours and ski for 2 hours. 
E)8 hours.

Quizplus · Accepted Answer

To find the consumer equilibrium, we need to compare the Marginal Utility per dollar for sailing and skiing. From the table, we see that the MU per dollar for sailing and skiing are 12 and 10 respectively. Since Sam has $80 to spend, the total expenditure on sailing and skiing cannot exceed $80. Let's assume Sam sails for x hours and skis for y hours. Then, the budget constraint is given by:

10x + 20y = 80
=> x + 2y = 8

To maximize utility, Sam should spend such that the MU per dollar for both activities are equal. Let's calculate the MU per dollar for each activity:

MU per dollar of sailing = 24 ÷ 2 = 12
MU per dollar of skiing = 20 ÷ 2 = 10

Since MU per dollar of sailing is greater than skiing, Sam should spend more on sailing. So, Sam should sail for x hours and ski for y hours such that the ratio of MU per dollar is the same as the ratio of prices. That is,

MU per dollar of sailing = MU per dollar of skiing
=> 12 ÷ 10 = 10 ÷ (20/x)
=> x = 4

So, Sam will sail for 4 hours and spend $40 (10 x 4) on sailing. The remaining budget of $40 will be spent on skiing at its price of $20 per hour, giving Sam 2 hours of skiing. Hence, the correct option is D - Sam will sail for 4 hours and ski for 2 hours.

Use the Table Below to Answer the Following Questions