# Econ2 HW4
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1.
( a )
The inputs used to produce goods and services
( b )
The marginal product of an input times the price of the output
2.
( a )
The milk market is perfect competitive to the firm since the it is a price taker.
( b )
The robot renting market is also perfectly competitive since the Smiling Cow Dairy is a price taker.
( c )
| Number of Robots | Marginal Product(gallons) | Value of Marginal Product($) |
| --- | --- | --- |
| 1 | 50 | 200 |
| 2 | 35 | 140 |
| 3 | 30 | 120 |
| 4 | 25 | 100 |
| 5 | 10 | 40 |
| 6 | 5 | 20 |

( d )
The firm should rent 4 robots because the value of marginal products of the first 4 robots are greater than the marginal costs(rental price $100).
3.
( a )
$Wage=ValueOfMarginalProduct=2\times(100-2L)=200-4L$
$L_{orchard}=50-\frac{Wage}4$
$L_{market}=L_{orchard}\times20=1000-5\times Wage$
( b )
$Wage=200-\frac{L_{market}}5=160$
Each firm hires $\frac{200}{20}=10\ labors$
$Q=100\times10-(10)^2=900\ apples$
$Profit=900\times2-160\times10=200$
( c )
$Wage'=4\times (100-2L)=400-8\times(\frac{200}{20})=320$
$Q'=100\times10-(10)^2=900\ apples$
$Profit=900\times4-320\times10=400$
Income of workers and orchard owners' both double as the price doubles.
( d )
$Wgae''=200-4\times \frac{200}{10}=120$
$Q=100\times 20-(20)^2=1600$
$Profit=1600\times 2-120\times 20=800$
$OriginalTotalIncome=200\times 20+160\times 200=36000$
$NewTotalIncome=800\times 10+120\times 200=32000$
The total income of the nation goes down.
4.
The value of the marginal product of the last worker is $12/hour.
The last worker produces $\frac{12}6=2$ sandwitches per hour
5.
( a )
Hire the amount of workers such that the value of marginal product is equal to the wage rate.
( b )
$\frac{150}{30}=5$
( c )
Labor market
Demand
The equilibrium wage is determined by the supply and demand of labor. Each firm than use the market wage and their demand to set their quantity of employment.
( d )
Labor market
Demand
Labor supply shifts to the left, causing equilibrium wage to rise. The marginal product of labor rises as the wage rises.