Question

Hugh, Frank, and Luis are the only three buyers of gold in a small mining town. Their inverse demand functions for gold are as follows: 480.00 48.00 x Qn, Hugh: p Frank: p 80.00 - 8.00 x Qf, Luis: p 20.00 - 2.00 x QL QH.QF, and are the quantities (in ounces) demanded by Hugh, Frank, and Luis, respectively Below, give all answers to two decimals. 1st attempt See Hint (1 point) Part 1 $20.00. The total ounces of gold demanded in this market is Suppose the price of an ounce of gold is p = See Hint (1 point) Part 2 Suppose the quantity demanded of gold in this market is 16.50 ounces. Then the market price of an ounce of gold must be $

Answer 1

Answer:

Explanation:

Hugh p= 480 - 48Qh

Frank p= 80 - 8Qf

Louis p= 20 - 2Ql

1. price of an ounce of gold = $20

Hugh will demand: 20 = 480 - 48Qh; Qh = 460/48 = 9.58 ounce

Frank will demand: 20 = 80 - 8Qf; Qf = 60/8 =7.5 ounce

Louis will demand: 20 = 20 - 2Ql; Ql = 0 ounce

Total demand = 9.58+7.5+0=17.08 ounce

2. quantity demanded of gold in this market is 16.50

Hugh Demand function: p=480-48Q , Q=10-p/48

Frank Demand function: p=80-8Q , Q= 10-P/8

Lius Demand function: p=20-2Q , Q= 10-p/2

Hugh will demand 0 quantity at , p=480-48*0 = $480

Frank will demand 0 quantity at , P=80-8*0 = $80

Lius will demand 0 quantity at , p=20-2*0 = $20

So when Price is between 80 to 480 only Hugh will participate in market. The demand function will be Q= 10-P/48

When Price is between 20 to 80 only Hugh and Frank will participate in market. The demand function will be Q=10-p/48 + 10-P/8   = 20-7p/48

When Price is between 0 to 20  all three will participate in market. Hence demand function will be Q=20 - 7p/48 + 10 - p/2  = 30 - 31p/48

When Demand is 16.5 ounce and if Price is between 80 to 480, then 16.5=10-P/48

P/48=-6.5

This is not possible

When Demand is 16.5 ounce and if Price is between 20 to 80, then

16.5=20-7p/48

7p/48 = 20-16.5

p = 48*3.5/7 = $24

Market price of an ounce of gold must be $24