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The elasticity of demand is calculated by,
Now to calculate the demand function , we equate the formula of elasticity to the given elasticity function, separate and then integrate.
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- A major South African city generates electricity and sells it to its consumers. The city faces competition from independentrenewable power producers who also have licences to sell electricity to the public. The city however has cost advantagesdue to its size, but it is concerned of the political and economic ramifications of raising its tariffs, in these uncertaineconomic times. As a result, it is highly likely that tariffs will remain unchanged over the next financial year. The city’smarginal revenue is given as R3 000, and its costs are given as follows:TC = R82 000 + R1 000 + 0.01q2 MCMC= R1 000 + R0.02q4.1 Assess the efficiency arguments in favour of and against the renewable energy generation in SouthAfricaConsider the binary variable version of the fixed effects model with an additional regressor, D1; that is, let Yit = β0 + β1Xit + γ1D1i + γ2D2i +...+ γnDni + ui.a) Suppose that n = 3. Show that the binary regressors and the “constant” regressor areperfectly multicollinear; that is, express one of the variables D1i , D2i, D3i, and X0it as aperfect linear function of the others, where X0it = 1 for all i,t.b) Show the result in (a) for general n.c) What will happen if you try to estimate the coefficients of the regression by OLS?Discuss the impact of COVID-19 in the Philippine
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- Consider the “Trip Logistic” example discussed in class (i.e. base case). Please solve the same problem with each of the following changes, and compare the results with those of the basecase: a) The spot market price (in period 0) is reduced to $0.55 per sq. ft. per year. Assume that everything else remains the same as the base-case. b) There is a lower demand uncertainty: Demand can go up by 5% with p= 0.5 or down by 5% with 1 − p= 0.5. Assume that everything else remains the same as the base-case.The travel time (t) on the segment of a highway connecting city A with city Bhas been observed to follow the equation below, as a function of traffic flow(v): t = 15 + 0.02v, where t and v are measured in minutes and vehicles perhour, respectively. The demand function for travel connecting the two cities isv = 3500 – 120t.a) Determine the equilibrium time and traffic flow.b) If the length of the highway segment is 30 kilometres, what is the averagespeed of vehicles traversing this segment at equilibrium conditions?You are hired as a consultant at a revenue management firm and one of ourrecent clients wished to determine the optimum price for their consumer electronics product.The cost of the product is $100 and before retaining us, they had been selling the product at$200 because it felt like a nice round number. The current sales volume is 1000 units peryear. We examined the market preferences and buying behavior, and concluded that thiscompany’s marketplace has a price elasticity of 1 (i.e. Assume that an x% change in pricewill result in an x% change in sales volume for any x). What is the optimal price thatmaximizes total profit for this company? What are the sales volume, total revenue and totalprofit at the optimal price?
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