Assist, with these attached questions.

Consider an economy with a representative consumer like the one described above, and a representative firm like The production function of the firm is given by zF (K, N) where: F (K, N) = K?N ? and ? + ?

a) (2.5 points) The equilibrium rental rate must be such that the demand and supply of capital are equalized. Find the equilibrium rental rate. Hint: You can express the equilibrium rental as a function of the wage. For this is is useful to use the FOC of the firm with respect to capital.

b) (2.5 points) The equilibrium wage must be such that the demand and supply of labor are equalized. Find the equilibrium wage. Hint: You can get an easier expression for the labor demand when you use the labor demand as a function of capital (obtained by combining the firm's FOC) and set capital to its market clearing value. Then you can solve for the wage. Remember to replace by the equilibrium interest rate from the previous point.

c) (2.5 points) With the equilibrium prices solve explicitly for the equilibrium labor. Hint: You can get a better expression for the equilibrium labor using the labor supply and replacing by the wage you obtained above. d) (2.5 points) In equilibrium, what happens to the wage, interest rate, labor and consumption when the government increases the labor taxes? Hint: Find out first what happens to the wage, and then use your result for the equilibrium interest rate to find out what happens to that variable. The effect on labor can be obtained directly from your answer to (c) or from the FOC of the firm with respect to labor. Finally, get the effect on profits before finding out the effect that extra taxes have on consumption.

(Production function) Condsider a representitive rm with a. production function which is ( i) twice continuously dierentiable; (ii) exhibits positive and diminishing marginal product and (iii) has constant return to scale: Y = F(K, L) (1) Given the capital rental price R and the wage to, and the good price P is normalized to 1, the rm can choose K and L to maximize its prot: 1}1{acF(K, L) RK 10L (2) 9.)The Mumfords had the following expenditures for 2019: Courtney's contributions to her traditional IRA $6000 Net gamabling loss 1000 Life insurance premiums 2700 Medical and dental expenses not covered by insurance 16612 Taxes: Ad valorem taxes on personal residence 4100 State and local sales taxes from receipts 2800 6900 Interest on home mortgage reported on form 1098 4000 Cash contributions: Feeding south dakota (EIN 36-3293534) 1750 South dakota governor's election campaign fund 300 2050 The $1,000 net gambling loss for 2019 is the difference between the Mumfords' gambling winnings of $1,200 and losses of $2,200. The life insurance premiums relate to the universal life insurance policies that Matthew and Courtney own. The first beneficiary on both policies is the other spouse, with the second beneficiaries being the children. Included in the medical expenses are $1,200 incurred in 2018, which were paid in early February 2019. While South Dakota does not impose income taxes on individuals, it does impose sales taxes. The Mumfords can substantiate the $2,800 in sales taxes paid based on their purchase receipts for the year. The local sales tax rate in Sioux Falls is 2%. (Hint: Be sure to check to see if the Optional Sales Tax Tables provide the Mumfords with a greater deduction.) Courtney contributed to the governor's campaign fund because she thinks her influence was key in getting the Minnehaha County land rezoned for commercial use (see item 4 above). 10.]The Mumfords maintain a household that includes their two children, Nickolas (age 16) and Kaleigh (age 19). Nickolas is a junior in high school and a talented wrestler. In hopes of competing at the state tournament, all of his free time is consumed with weight training and wrestling practices. Kaleigh graduated from high school on June 7, 2018, and is undecided about college. She is an accomplished vocalist and during 2019 earned $7,200 performing at various events (e.g., weddings, funerals). Kaleigh placed most of her earnings in a savings account for future use and kept only a small amount to spend on herself. 11.)Matthew's Form W-2 from The Pour House shows $15,800 withheld for Federal income tax. The Mumfords also made estimated tax payments to the IRS totaling $5,000 for 2019