UH UH m M NNNN 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) Equilibrium Price and Quantity lpha Pd = a: + a Pf = A + 5QI lambda . . . . . delta Equlhbrlum Condltlon: P: = If For the demand and supply equations above and parameters to the right, Equilibrium Price Equilibrium Quantity Maximum Total Surplus Dead Weight Loss when government restricts output to be (2:400 12'," = arr2'39)\" alpha P: = 2.6an beta I lambda Equilibrium Condition: Pf = P: delta For the demand and supply equations above, Equilibrium Price Equilibrium Quantity Price 8r. Quantity Adjustments to Demand or Supply Shocks Consider a market in equilibrium wherein e +18% shock to demand occurs. Assume also that the supply function is highly elastic (Es = 5) and the demand function is also highly elastic (Ed = -7). What is the approximate % change in equilibrium price? What is the approximate % change in equilibrium quantity? Consider a market in equilibrium wherein a 20% shock to supply occurs. Assume also that the demand function is highly inelastic (Ed = -0.75) and the supply function is also highly elastic (Es = 3.25). What is the approximate % change in equilibrium price? What is the approximate % change in equilibrium quantity? 50 -0.0166667 33.333333 0.0111111 65.780621 -0.0006667 30.326533 0.001 Optimal Pricing Consider two products of equal marginal cost of $10. Product A has an elasticity of demand of -2 (Ea = -2.0) and Product B has an elasticity of demand of -11.0 (E. = -11.0). What are your optimal prices of Product A and Product B? 3 27) Optimal, Profit Maximizing Price of Product A? 3 28) Optimal, Profit Maximizing Price of Product B? Profit Maximization Total Cost (TC); Total Revenue (TR) Let TC =0.125 Q' + 100 Q and TR = -0 .075 Q2 + 200 Q 2 29) What is the profit maximizing quantity? 2 30) What is total revenue at Q profit max? 31) What is Price at the profit maximzing level? 2 32) What is profit at Q profit max? 33) T/F The Profit Function can be written as Profit = TR - TC = 100 Q-0.2 Q? 34) T/F Taking the derivative of the Profit Function, setting it equal to zero and solving for Q yields the same profit maximizing Q that we get from a TR-TC perspective. 2 35) What is profit at five units less than the profit maximizing Q? 2 36) What is profit at five units more than the profit maximizing Q? 2 37) What is point elasticity of demand at the profit maximizing Q? 1 38) What is the Mark-up factor value?1 38) What is the Mark-up factor value? 1 39) What is MC * Mark-up factor equal to at the profit maximizing Q? 1 40) T/F This is the same price as reported in 24) above. The "Internal Rate of Return" is that rate of interest that equates the cost of an investment with the present value of a future stream of earnings. Calculations can be performed in the cells below this problem set. 1 41) An initial investment of $5000 in the base year "0" yields a constant $1000 per year for 10 years. What is the "internal rate of return?" 1 42) An initial investment of $5000 in the base year "0" yields a net return per year for 10 years, increasing each year such that the sum of the nominal returns equals $10,000 for the 10 years, as in the prior problem. The return per year "t" is NRt = 175 + 150*t. Thus, in year 10 the net return is $1675. What is the "internal rate of return?" 1 43) An initial investment of $5000 in the base year "0" yields a net return per year for 10 years, declining each year such that the sum of the nominal returns equals $10,000 for the 10 years, as in the prior problem. The net return per year "t" is NR, = 1825 -150*t. Thus, in year 10 the net return is $325. What is the "internal rate of return?" 1 44) T/F Internal rates of return are higher when the net returns are concentrated in early years. Trial Net Present Interest Year Revenue Value Rate 5000 0.05 1000 1000 1000 1000 1000 1000 1000 1000 1000 10 1000