Search
Show that the quantity of labor(X1) and capital(X2) that a firm demands decreases with a factor’s own factor price (w for labor and r for capital) and increases with the output price (P) when the production function is a Cobb-Douglas of the form q=AX1^αX2^β
As quantity of a variable input increases, explain why the point where marginal product begins to decline is reached before the point where average product begins to decline. Also explain why the point where Average product begins to decline is reached before the point where total product begins to decline.
Qr-200-0.01P+0.005PM-10PG+0.017 +0.0034.
where
Q=quantity purchased,
P= the average price of Toyotas,
PM= the average price of Mazdas,
P= the price of gasoline,
I= per capita income, and
A = dollars spent annually on advertising.
a. Find the point price elasticity of demand for the Toyotas if Pr= $25,000, PM= $20,000, P=$1.00, 1-$15,000, and A = $10,000.
b. Is the price elasticity of demand elastic, unitary elastic, or inelastic? Why?
c. Find the arc cross elasticity of demand for Toyotas and Mazdas between PT=$20,000 and PM $22,000. (All other figures except P, remain the same as in part (a).) d. Are Toyotas and Mazdas substitutes or complements? Why?
a. Based on the estimated demand curve, write the equations for Alpha's
(1) Average revenue,
(ii) Total revenue, and
(iii) Marginal revenue.
b. What will be the maximum total revenue per week that Alpha can obtain from sales of its product? (Give the exact dollar amount and explain how you determine it.)
c. Calculate the point price elasticity of demand for Alpha's product when Q= 1,600. Is demand elastic or inelastic at this quantity? How do you know?
d. Calculate the arc price elasticity of demand for Alpha's product between Q== 1,000 and Q=1,100. Interpret your result and relate it to what will happen to total revenue if Alpha is initially at Q = 1,000 and decides to cut price to increase its sales from 1,000 to 1.100 units.
demand function (number purchased annually) for their (Brand X) automatic
washer is as follows:
Qx=197,000-100P+50Py+0.0251 +0.02A + 10,000P
where
ex- quantity purchased,
Px price of the company's washer,
Py = price of a major competitor's washer,
I= average household income,
A= annual dollars spent on advertising
PL = cost of doing one load of wash in self-service laundry.
a. If Py=$300, I=$40,000, A-$200,000, and P =$.30, find the price elasticity of demand between Py=$350 and P$400. (When P = $400, with the values of the other variables as given above, then Qx = 180,000.)
b. Is EpX elastic, inelastic, or unitary elastic? Why? If the price is cut, does total revenue increase, decrease, or not change?
c. Find the income elasticity of demand for Qy, given Py=$400. The other vari ables are as given in part (a). Interpret your answer-that is, what does it say, if anything, about the demand for Brand X washers?
a. Find the new quantity of rooms rented per night if the Hotel Madrileà ±a low ers its price to $80 and its price elasticity of demand is -1.5.
b. After the Hotel Madrileà ±a lowers its price, a little pensià ³n across the street lowers its room rate from $35 to $30 per night. Find the new quantity of rooms rented per night for the Hotel Madrileà ±a after the pensià ³n lowers its price if the cross price elasticity between the price of the pensià ³n's rooms and the quantity demanded of the Madrileà ±a's rooms is 1.0. (Hint: Use the num ber you found in part (a) as Q, in this problem.)
c. What will be the final effect of the price decreases in parts (a) and (b) on Hotel Madrileà ±a's total revenue?
Let the production function of a firm is given as
𝑞=(𝑥0.5 +𝑦0.5)2
Where 𝑥 and 𝑦 are inputs and 𝑤𝑥 is the price of input 𝑥 and 𝑤𝑦 is the price
of input 𝑦.
a) Assume the firm has a limited budget to spend on buying input. Find
the cost-conditional input demand function for each input.
b) Find the cost function of the firm.
With practical example. Discuss the following
1) Elasticity and income Elasticity of demand.
Ii) The relationship between price Elasticity, total revenue and marginal revenue.
III) The factors affecting price Elasticity of demand.
#339914 on Dec 2023