Going Green
There are two groups of consumers of solar panels in country S: 150,000 households who consider purchasing them because they care about the environment and 200,000 households who consider purchasing them because it is trendy (this is sometimes called the bandwagon effect). The demanded quantities of the solar panels are given by:
where is the price of a solar panel (in USD) and is the total quantity of solar panel users (in equilibrium, ). For simplicity, assume that , and can be non-integer.
The supply of the solar panels is perfectly elastic, . The market adjusts to the equilibrium in the following way. First, customers who care about the environment decide whether they will have solar panels. At every step after that, customers from the 'trendy' group observe the quantity of solar panels around and decide whether they will have solar panels based on this observation. This goes on until everyone is happy with their choice.
(a) (5 rp) How many solar panels will be purchased?
Quantity demanded by those who care is . The number of panels to be purchased by the second group in the first period: . With this, becomes approximately and should increase further: . The process will continue until the equilibrium is reached. In equilibrium, , so
One can rewrite it with and get . This is a quadratic equation solved by . The second one is negative; the first one will result in . , so is , but there are only households in this group, so actually and .
(b) (15 rp) The government introduces a per-unit subsidy s = $5,000. Calculate the quantity of solar panels in equilibrium.
Now the price for consumers is , and . There are even more consumers at the initial stage, so the 'bandwagon' segment will be even more willing to join, everyone there will join again. So, .
(c) (10 rp) After the equilibrium from (b) is reached, the government surprisingly eliminates the subsidy. Customers have the opportunity to return the once-purchased solar panels and get $25,000 refunded (and indeed do this if their willingness to pay is below 25,000 per panel). Find the new equilibrium quantity of installed solar panels. Is your answer the same as in (a)? Why or why not?
According to the described mechanism, those who care will adjust first and return back to . So, the equilibrium condition will be the same as in (a), so as the result.