average variable cost (Acup C) average total cost (ATC) and avorage fixed cost (AFC) What is the minimum -cost output? b) For eachlevel of output, calculate this manufacture 5 marginal cost (MC) QUESTION THREE (5 Marks) a) Short run production function is given by Q=90L^2-L^3 Find the level of labor where AP is maximized. b) if the total cost function of producing a commodity is given as TC=4q2+2a WherebyTC=totalcost,q=output Find-Marginal Cost c) Consider the following short run production function: Q=6L^2-4L^3 (i) Find the value of L that maximizos output. (ii) Find the value of Lithat maximizes average product QUESTION FOUR (5 Marks) Consider the following policies each of which is almod at reducing violent crime by reducing the use of guns. Illustrate each of these proposed policies in a supply and- demand of the gun (1) a taxon gun buyers (ii) a taxon gur sellers (iii) a price floor on guns (iv) a taxon ammunition (bullets)

##Step 1: Find the labor that maximizes AP<br />###Average product (AP) is given by $AP = \frac{Q}{L}$. In this case, $AP = \frac{90L^2 - L^3}{L} = 90L - L^2$. To maximize AP, we take the derivative with respect to L and set it equal to zero: $\frac{d(AP)}{dL} = 90 - 2L = 0$. Solving for L, we get $L = 45$.<br />##Step 2: Calculate Marginal Cost<br />###Marginal cost (MC) is the derivative of the total cost (TC) function with respect to quantity (q). Given $TC = 4q^2 + 2a$, where 'a' is likely a typo and should be 'q', the corrected TC function is $TC = 4q^2 + 2q$. Therefore, $MC = \frac{d(TC)}{dq} = 8q + 2$.<br />##Step 3: Find L that maximizes output<br />###To maximize output Q, take the derivative of the production function with respect to L and set it equal to zero: $\frac{dQ}{dL} = 12L - 12L^2 = 0$. Factoring out 12L, we get $12L(1 - L) = 0$. This gives two solutions: $L = 0$ and $L = 1$. Since $L=0$ means no output, the value that maximizes output is $L = 1$.<br />##Step 4: Find L that maximizes average product<br />###Average product (AP) is $AP = \frac{Q}{L} = \frac{6L^2 - 4L^3}{L} = 6L - 4L^2$. To maximize AP, take the derivative with respect to L and set it equal to zero: $\frac{d(AP)}{dL} = 6 - 8L = 0$. Solving for L, we get $L = \frac{6}{8} = \frac{3}{4} = 0.75$.<br />##Step 5: Analyze Gun Control Policies<br />###(i) Tax on gun buyers: This decreases demand, shifting the demand curve left.<br />###(ii) Tax on gun sellers: This decreases supply, shifting the supply curve left.<br />###(iii) Price floor on guns: This sets a minimum price above the equilibrium, leading to a surplus of guns.<br />###(iv) Tax on ammunition: This decreases the demand for guns (as they become less useful), shifting the demand curve left.<br /><br /><br />#