Question

Q5 (6 pts). Given the following linear supply and demand in standard form Supply:-2P + 4Q =-12 Demand: 5P +200 150 Find the inverse linear demand and supply [Price as a function of Quantity Q f(P)], the equilibrium price [P*] and quantity [Q1. Graph the demand, supply and the equilibrium point (P* and Q) in the supply-demand diagram Choose the correct answer (Showing the appropriate steps) a) Supply: P 20 6, Demand: P40 30, P 14,Q4 b) Supply: P-4-3, D Q + ' , P"-14,0% 4 c) Supply: P-|Q + 6, Demand: P =-10-2, p. = 4,Q' = 14 emand:P-_ d) Supply: P-2Q + 6, Demand: P =--Q + 30,P" = 14, Q. 4 (Hint: convert them into the slope-intercept form)

Answer 1

Solution:

We are given the supply and demand functions in standard forms. The inverse supply and demand functions are simply price, P as a function of quantity, Q.

Finding inverse supply function:

Supply: -2P + 4Q = -12

Adding 2P on both sides, -2P + 4Q + 2P = -12 + 2P

This gives us 4Q = -12 + 2P

Now, adding 12 on both sides: 2P = 4Q + 12

Finally, dividing both sides by 2, we get P = 2Q + 6. This is our inverse supply function.

Similarly, Demand: 5P + 20Q = 150

Subtracting 20Q from both sides, 5P = 150 - 20Q

And dividing both sides by 5, we get P = 30 - 4Q. This is our inverse demand function.

(From options, by now one can see the correct option is (a)).

Finding equilibrium prce, P* and quantity, Q*:

In equilibrium, the two curves (demand curve and supply curve) intersect, as quantity demanded must equal quantity supplied.

Then, intersection of the two curves occur where, 2Q* + 6 = 30 - 4Q*

2Q*+ 4Q* = 30 - 6

6Q* = 24

Q* = 24/6 = 4 units

So, equilibrium price, P* (found by substituting Q* in either of inverse demand function or inverse supply function):

P* = 2(4) + 6 = 8 + 6 = $14

So, correct option is (a).

Figure marking the two curves and the equilibrium point:

Taking price, P on the vertical axis and quantity, Q on the horizontal axis, for the supply curve: horizontal intercept = -12/4 = -3, and vertical intercept = -12/-2 = 6

For demand curve, horizontal intercept = 150/20 = 7.5, vertical intercept = 150/5 = 30

Price, P 30 Demand curve 24 21 Supply curve 15 P 14 12 -3 2-1 012 3 45 678 9 10 Qantity, Q