22 Homers boat manufacturing plant production function yK L is the square root of K times square root of L to the fifth where K is the number of hydraulic lifts and L is the number of labor hours he e

To determine if the production function exhibits increasing, decreasing, or constant returns to scale, we need to look at how the output changes when all inputs are increased by a certain percentage.

Let's say we double the inputs:

y(2K, 2L) = sqrt(2K) * sqrt((2L)^5)

= (sqrt(2K) * sqrt(L^5)) * (sqrt(2L)^5)

= sqrt(2) * y(K, L)

Since the output has doubled, this production function exhibits increasing returns to scale.

If Homer increases his use of labor hours and hydraulic lifts by 10%, his new inputs would be:

K = 55

L = 22,000

His new production would be:

y(1.1K, 1.1L) = sqrt(1.1K) * sqrt((1.1L)^5)

= (sqrt(1.1K) * sqrt(L^5)) * (sqrt(1.1L)^5)

= 1.1 * y(K, L)

So his production would increase by 10%.

If Homer increases his use of all inputs by 10%, his costs and production will both increase by 10%.

His new inputs would be:

K = 55

L = 22,000

His new production and costs would be:

y(1.1K, 1.1L) = 1.1 * y(K, L)

Revenue = $75,000

Profit = Revenue - Costs

= $75,000 - (1.1 * Cost)

Since his costs and revenue both increase by 10%, his profits will remain the same