1. A firm's production technology is Y = A * K^0.25 * L^0.75, where the technology level A=8. For such a production function the marginal product of capital is MPK = 0.25 * 8 * K^-0.75 * L^0.75

The firm is stuck with K=81 but is flexible on workers. If the price of the firm's output is P=20 and the cost of a unit of capital is R=8.33, how many workers should the firm have?

Round your answer to the whole worker.

The answer is 10. I just need to know how to solve it

these bottom two are solved I am just struggling with how to graph the consumption function and the breakeven condition for this problem and to Point out the income and consumption values relevant for these problems: only 3 and (3a)

3. The marginal propensity to consume (MPC) is 0.75, which means that households spend 75% of each additional dollar of income. The starvation-level consumption is 6, which means that households will consume at least 6 dollars, regardless of their income.

Therefore, the amount that households will save can be found by subtracting their minimum consumption level from their gross income, multiplying the difference by the MPC, and subtracting the lump-sum tax:

Savings = (1 - MPC) * (Gross Income - Starvation-level Consumption) - Lump-sum Tax

Savings = (1 - 0.75) * (40 - 6) - 10

Savings = 0.25 * 34 - 10

Savings = 1.5

Therefore, households will save $1.5.

3. a) How should the lump-sum income tax change to allow households to save 3?

To allow households to save $3, we need to solve for the new lump-sum tax that will make this possible.

Using the same formula as in part (3), we can set the savings equal to 3 and solve for the lump-sum tax:

3 = (1 - MPC) * (Gross Income - Starvation-level Consumption) - Lump-sum Tax

3 = 0.25 * (Gross Income - 6) - Lump-sum Tax

3 = 0.25 * Gross Income - 1.5 - Lump-sum Tax

Lump-sum Tax = 0.25 * Gross Income - 4.5

Therefore, the lump-sum tax should be set to 0.25 times the gross income minus 4.5 to allow households to save $3.