A consumer may consume food x and hours of leisure time h. The price of one...

A consumer may consume food x and hours of leisure time h. The price of one unit of food is $1. Initially, the consumer has no money and 24 hours of spare time that she may devote either to work, or to leisure. The consumer earns wage rate s per hour for the first five hours of work, and s′ per hour for additional overtime hours. She also faces a tax rate of t percent on labor income earned above amount M. Draw the consumer’s budget set for the following two cases of parameter values:

1. s=$6,s′ =$8,t=30%,M=$70; 2. s=$5,s′ =$7,t=40%,M=$20.

Which bundle(s) correspond to kink(s) of the consumer budget constraint?

Solutions

Expert Solution

Normal wages = Normal rate × 5 hours = $6 × 5 = $30

Bonus wages = Bonus rate × (24 – 5) hours = $8 × 19 = $152

Total wages = Normal wages + Bonus wages = $30 + $152 = $182

Tax = (Total wages - $70) × 0.30 = ($182 - $70) × 0.30 = $33.6

Budget = Total wages – Tax = $182 - $33.6 = $148.4

Given, $1x = $148.4

Therefore, x = $148.4 / $1 = 148.4

The required graph is as below:

Normal wages = Normal rate × 5 hours = $5 × 5 = $25

Bonus wages = Bonus rate × (24 – 5) hours = $7 × 19 = $133

Total wages = Normal wages + Bonus wages = $25 + $133 = $158

Tax = (Total wages - $20) × 0.40 = ($158 - $20) × 0.40 = $55.2

Budget = Total wages – Tax = $158 - $55.2 = $102.8

Given, $1x = $102.8

Therefore, x = $102.8 / $1 = 102.8

The required graph is as below:

Rahul Sunny answered 1 year ago

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