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Assume that the production function of your country at period t is given by Y(t) = A(t)K(t)"L(t)1-", where a = 0.3, Y is output, K is capital, L is labor, and A is the technological level of the country. Assume for now that A(t) = 1 in any period. Also assume that the depreciation rate of capital is o =0.01. 1. Write the production function in per capita terms. 2. Write the main equation of the Solow model (in per capita terms) using this production function.6. Now let's consider a Solow growth model where technology is constant and does not evolve over time. The production function is given as Y (t) = F(A, K(t), L(t) ) = AK(t) " L(t) 1 -a Where Y is output, A is technology, K is physical capital, and L is labor. Labor grows as a rate of n and technology is constant, i.e. g = 0 Suppose further that capital accumulation is given as K = SF(A, K(t), L(t) ) - 6K(t) a. Defining k = *, prove that y = = = Aka b. With the same definition of k, find the equation for k c. Find steady state levels of k (in terms of given parameters) d. Find steady state level of y e. Find steady state level of cAn industry's inverse demand was PD = 20 - 6.10 and its inverse supply was P5 = 4 + I110. a. Calculate the consumer surplus, producer surplus, government revenue and deadweight loss for taxes of 54, SB, 512 and $16 per unit sold. o. Graph govern merrt revenue and dead weight loss as functions of these tax rates. c. What tax maximizes government revenue? 1) (4 pt) Consider a firm that produces good r from labor and is the only demander of labor. This firm is a price taker on output market and a price maker on labor market. The output price is 2 per unit. The production function of the firm is given by (L) - 50L - 1.5L', The labour supply function is L,(w) = 0.5w. a) Find equilibrium wage rate and employment. Illustrate graphically. b) Analyze the effect of imposition of a minimum wage rate at w = 28. Illustrate by graph. c) Repeat part (b) for the minimum wage rate set at w) = 46. d) "When firms have some monopsony power, a minimum wage slightly above the free market equilibrium is good for jobs - it offsets the distortion caused by the market power of employers - but a minimum wage substantially above the free market equilibrium is bad for jobs." - BVFD, p.239. Find all possible levels of minimum wage that are bad for jobs in considered economy