Question

QUESTION 1

James mainly sells confectionery items, newspapers, magazines and cigarettes in

his convenience store. Noting his small business is not thriving, he thought of

selling hot pies and rolls too.

Suppose the total cost function for rolls and pies is,

TC = 800 + 53?, ? = ?1 + ?2

where ?1 and ?2 denote the quantities of rolls and pies respectfully. If ?1 and ?2

denote the corresponding prices, then the inverse demand equations are:

?1 = 73 − ?1 and 0.5?2 = 100 − ?2

REQUIRED:

d) If James decides to make a total of 51rolls and pies per day and charges

different prices as above (that is, ?1 ≠ ?2 ), how many of rolls and pies each

should he make in order to maximize the profit of a particular day? Estimate the

increase in maximum profit which results when the total number of rolls and pies

per day (51) is increased to 52 [note: assume second-order conditions are

satisfied].

e) The COVID-19 pandemic saw the lockdown of many cities to reduce the

spread of the virus. This unprecedented move can be viewed as a negative demand

shock. Explain the impact of the lockdown of the city where James’ convenience

store is located on the demand functions of rolls and pies (half a page maximum).

Answer 1

d) when different prices are charged by James for rolls and pies----

profit maximising -----Number of rolls =10

-------Number of pies=41

Calculations-----

The profit maximising point occurs where MR=MC

TC=800+53Q

MC=53

*Profit maximising point in case of rolls-------

Q=73-P1 ,P1= 73-Q1

TR=73Q-Q1*Q1

MR=73-2Q1

At equilibrium------

73-2Q=53

Q=20/2=10 rolls

* profit maximising point in case of pies---------

.5Q2=100-p2 Or P2=100-0.5Q

TR= 100Q-0.5Q2

MR=100--Q2

At equilibrium-----

100-Q2=53

Q2=47pies

As , Q=Q1+Q2=51

As Q1=10., so ----

Q2=51-10=41 pies

# Increase in profits if quantity of rolls and pies is increased to 52 numbers profit increases by $6[from 386 to 392]

Initial profit(Q=51)-----

TR1+TR2--TC

# Calculating TR1------------

finding P and AC of rolls-----

p1=73-10=$63
TR1=P1*Q1= 63*10=$630

#Calculating TR2---------

Q2=41

p2=100-.5*41=79.5$

TR2=41*79.5=$3259.5

# calculating TC----

TC= 800+53*51=$3503

profit= 630+3259-3503=386

# PROFIT AFTER Q=52-------

finding TR2-------

Q2=52-10=42 pies

p2= 100-0.5Q2= 100- .5*42=$79
TR2= 42*79=$3318
TC= 800+53*52=3556$
profit= 630+3318-3556=$392

Increase=392-386=$6
e) Negetive demand shock implies decrease in the demand for rolls and pies in the markett