Equilibrium point. Use the models constructed in Problem 1 to find the equilibrium point. Write the equilibrium price to the nearest cent and the equilibrium quantity to the nearest unit.
Problem 1
Supply and demand. A cordless screwdriver is sold through a national chain of discount stores. A marketing company established price–demand and Price–supply tables (Tables 1 and 2), where x is the number of screwdrivers people are willing to buy and the store is willing to sell each month at a price of p dollars per screwdriver.
(A) Find a logarithmic regression model (y = a + b ln x) for the data in Table 1. Estimate the demand (to the nearest unit) at a price level of $50.
Table 1 Price–Demand
x
p = D (x)($)
1,000
91
2,000
73
3,000
64
4,000
56
5,000
53
(B) Find a logarithmic regression model (y = a + b ln x) for the data in Table 2. Estimate the supply (to the nearest unit) at a price level of $50.
Table 2 Price–Supply
x
p = S(x)($)
1,000
9
2,000
26
3,000
34
4,000
38
5,000
41
(C) Does a price level of $50 represent a stable condition, or is the price likely to increase or decrease? Explain.
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