Question

hi! this question is including the solution. In part (e), the answer of the value of per HP is $4.14, but how could we define it is over or underestimate? why in this question is underestimates? thank you!

2. There are two types of car drivers, Leadfoots and Slowdrivers. To make the math simple, assume there is 1 of each type of customer. Cars differ in their price P and horsepower HP. Each customer is going to buy 1 car, but it can have a different level of horsepower and price. The total WTP for a car for a Lead- foot is WTP 150HP .1H P2. The total WTP for a car for a Slowdriver is WTP = 150HP-.15HP2 wTPis specified in dollars. There are two car markers, Todge and Doyota. For simplicity, assume that they price at cost: each firm will sell a car for the total cost of making it. They choose HP to maximize value (so marginal WTP will equal marginal cost). Todge is re- ally good at making fast cars. Doyota makes lovely cars, but it is hard for them to make their cars really fast. Todge's total cost of making a car (in dollars) is TC 0.025HP2. Doyota's total cost of making a car (in dollars) is TC = 0.45HP2 (a) Assume for simplicity that each car maker makes 1 car only, and that each carmaker is going to specialize in selling cars to one type of customer. Which carmaker should sell to Leadfoots and which should sell to Slowdrivers in equi- librium? Explain in 1 sentence why it would be inefficient if the carmakers swapped customers. Todge sells to Leadfoot, Doyota sells to Slowdriver. If the sellers swap, Lead- foot will have to buy more HP at higher price. (b) What is the price and HP of the car that Todge will sell? What is the price and HP of the car that Doyota will sell? (Assume that the automaker chooses HP to maximize total surplus and then charges the full cost of making the car with that level of HP. This leads to an efficient choice of HP.) MwTPLF HPLP 600 NYT PSD HPSD 125 TCrodge = 0.025 * 600-9000, TCDoget.-0.45 * İ 252-703 1.25 150-02HP, MCTodge 0.05HP. 150-0.2HP = 0.05HP, 150-03HP, MCDoyota = 0.9HP. 150-0.3HP = 0.9HP, 1.MWTP-MC to find HP for each brand 2.sup the HP into the TC function (c) In class, we discussed using hedonics to understand WTP. One obvious ver- sion of this is to calculate the marginal WTP for the amenity (in this case, HP). What is the marginal WTP at the equilibrium choice for Leadfoots and Slowdrivers? marginal WTP- MWTP (sup HP into equation(HP found in part b)) MwTP.F = 150-0.2 * 600 = 30. MWT PSD 150-0.3 125 112.5. (d) Which one is larger? Is this surprising? Explain what this has to do with sorting of customers across the two firms. SD's MWTP is larger. This should not be surprising as we are comparing MWTP at two different HP levels. SDs are sorted into an equilibrium with low HP. So, their MWTP should be larger at lower HP. (e) Now suppose that you used the difference in HP and the difference in price across the two product to value HP. What would estimate the value of HP to be? Is this an over or underestimate of the value of HP? (2 points) MWTP 9000-7031.25 125 4.14 This underestimates the value of HP.

Answer 1

In part B we have found the value of Hp by equating MWTP (LF)= MC (Todge) for which we have found the value of Hp(Lp) to be 600. Similarly we have also found Hp (SD) to be 125.

Now in part C likewise at these two values of HPs we have found MWTP (LF,SD) to be 30 and 112.5. In part D we have mentioned the MWTP for SD (130) is higher as HP is lower i.e 125.

Now all these findings are actual finding. We know in econometrics term error= actual -fitted

***So here in part (e) we have found the value of HP I.e MWTP (hat) which is the estimated value of HP. Which we have found to be 4.14 which is much lower than the actual HPs which are 600 and 125. So here we have underestimated the value of HP so likewise if it were more than the actual finding it would have been over estimated value.