Please just do #2, starts with \" the market demand for food\".... PLEASE ANSWER
ID: 1201690 • Letter: P
Question
Please just do #2, starts with " the market demand for food".... PLEASE ANSWER ALL PARTS OF THE QUESTION THOROUGHLY WITH ALL STEPS. ANSWERS PARTS ON HOW MUCH HONEST AND DISHONEST PERSON CHARGES AND OTHER SUB QUESTIONS PLEASE!!!
Chrome File Edit View History Bookmarks People Window Help No Equities 66% H, Tue 6:05 PM a E eek-LSAT-Week LSAT Se x The Ideal Way toLaw School AppMy Pitt Home xProbiem set 5Problem set 5.pc xLSAT study guic x CDO 13.55 PART x fi Person1 Problem set 5- x Ahttps://courseweb.pitt.edu/bbcswebdav/pid-20745701-dt-content-rid-17504047-2/courses/2164UPITT-ECON-1100-SEC 1070/Problem%20set%205.pdf The market demand for food is Q = a-P, and the monopolist's marginal cost is c>0. Suppose the government sets a price ceiling equal to c. How much does the "honest" monopolist charge and supply? What does the "dishonest" monopolist charge beyond c in the form of bribes, and how much does he/she supply? Compare the profits of the honest and dishonest monopolist. Suppose the government allows the monopolist to charge d> c. What are the profits of the honest and dishonest monopolists? Under what conditions (if ever) does it pay to be honest? 2. 3. Be able to solve Perloff's solved problems 14.1,14.2,14.3 and 14.4 (DO NOT HAND THIS IN) 4. Perloff, pages 524-527, questions 2.2,4.1, 5.3 and 5.7.Explanation / Answer
Let us first define what does mean by ‘Honest’ and ‘Dishonest’ monopolist. We know from the basic structure of monopoly that the monopolist enjoys a great power over the market price of the product, that is, the firm is a price maker. So, the monopolist can charge whatever price they want as long as it maximizes its profit.
Now, if a government fixes a price ceiling, and the monopolist comply with the government’s decision by charging the ceiling price, irrespective of its loss would be considered to be a honest monopolist; whereas the monopolist which would charge more than the ceiling price by giving bribe to the government officials in order to retain his/her initial level of profit intact would be considered as a dishonest monopolist.
Now, the market demand function is given as, Q = a – P => P = a – Q
So, the revenue of the monopolist is, TR = P * Q = (a – Q) * Q = a Q – Q2
Thus, the marginal revenue of the firm is, MR = d(TR)/dQ = a – 2Q
The marginal cost of the firm is given as, MC = c > 0
Therefore, the monopolist’s profit maximizing condition of MR = MC, we get,
a – 2Q = c
This is the profit maximizing output produces by the firm.
The price charged for supplying this amount of output would be,
P = a – {(a – c)/2}
Now, if the govt. sets the price ceiling at P’ = c, then the honest monopolist will charge this price and would produce and supply, QH = (a – c) amount of output in the market.
So, the revenue earned by the honest monopolist would be, TRH = P’ * QH = c * (a – c) = ac – c2
Since, the MC of the honest monopolist is c > 0, so the TC of the monopolist would be, TCH = c Q + f; where ‘f’ is the fixed cost incurred by the monopolist.
So, for the honest monopolist, according to the equilibrium output, the total cost would be,
TCH = c * (a – c) + f = ac – c2 + f
Therefore, the profit earned by the honest monopolist would be,
H = TRH - TCH
H = ac – c2 – ac + c2 – f
H = -f
Thus, the honest monopolist would incur a loss by the amount of fixed cost.
Now, in case of the dishonest monopolist, he will try to retain the initial profit, so would charge the initial price, P = (a + c)/2. And according to this price, the output supplied by him would be,
QDH = (a – c)/2
So, the amount of bribe for per unit of output provided by the dishonest monopolist is,
P – c = (a + c)/2 – c = (a – c)/2
This is amount of price that the monopolist charges beyond the ceiling price (c) in order to provide the bribe.
Therefore, the revenue earned by the dishonest monopolist is,
TRDH = P * QDH = {(a + c)/2} * {(a – c)/2}
And the cost incurred by this monopolist would be,
TCDH = c * {(a – c)/2} + f
Thus, the profit earned by the dishonest monopolist would be,
DH = TRDH - TCDH
Since, a > 0, c> 0, so we could say, [(a – c)/2]2 > 0
If [(a – c)/2]2 > f, then the dishonest monopolist would make some profit and if [(a – c)/2]2 < f, then some part of the fixed cost incurred by the monopolist would get covered by [(a – c)/2]2.
Therefore, if we compare the honest and dishonest monopolist, we could say that the dishonest monopolist stays at a better position in every possible situation.
Now, the govt. decides that the monopolist could charge the amount d > c. For this new price, let us do the above explained procedure once again, starting with the honest monopolist.
The honest monopolist will charge P” = d > c. So, the quantity that he/she would supply would be,
QH’ = a – d
Therefore, the revenue earned by the honest monopolist would be,
TRH’ = P” * QH’
And the cost incurred by the monopolist would be,
TCH’ = c * (a – d) + f
So, the profit earned by this monopolist would be,
H’ = TRH’ – TCH’
Now for the dishonest monopolist, he/she would be charging the initial price, P = (a + c)/2, supplying the same quantity, QDH = (a – c)/2.
Since the cost structure for this monopolist remains same as before, the profit earned by him/her would be same as before. That is, the profit earned by the dishonest monopolist would be, DH = [(a – c)/2]2 – f.
In this case actually only the price that the govt. put ceiling on changes (increases to d > c), but since the dishonest monopolist never charge the ceiling price fixed by the govt., the factors like price charged, quantity supplied and the profit earned by this monopolist do not change. The only factor that changed is the bribe paid per unit of output [which is the difference between the price charged by the dishonest monopolist (P) and the ceiling price (d)].
These are the required profits of the honest and dishonest monopolists respectively.
Now, the condition under which we could say that it pays to be honest is that the profit earned by the honest monopolist exceeds the profit earned by the dishonest monopolist.
We had seen that for the ceiling price “c”, there is no way the profit earned by the honest monopolist could be greater than the dishonest monopolist; but for the ceiling price “d”, we could compare the profits as follows—
H’ > DH
Since the square-root of [2d – (a + c)]2 would become imaginary, so we will not find any such condition for which we could show that it pays to be honest.
Therefore, we could conclude that being honest does not pays off in this case.