9. Assume that the inverse demand function for a good is given by p=f (q)=25/(2+q³), where p denotes the price per unit of the good in dollars and q denotes the quantity demanded of the good. Find the rate of change of quantity with respect to price.

Q: A firm operates with the production function Q = K2L. Q is the number of units of output per day…

A:

Q: If consumption is $5 billion when disposable income is $0, and if the marginal propensity to consume…

A: Given: consumption = $5 billion disposable income = $0 marginal propensity to consume = 0.60…

Q: Suppose that the dollar cost of producing x washing machines is c(x) = 2000 + 100x - 0.1x2. a. Find…

A: Consider the given cost function.

Q: Suppose that the fixed cost for a prod- uct is $400 and the break-even quantity is 80. Find the…

A: Fixed cost of the product = $400⇒C(x)=ax+400Let us take the profit function as⇒P(x)= bx+cAnd the…

Q: Suppose the demand function for a product is given by the function: D(q) = 0.011q + 37.4 Find the…

A: Given: The demand function is D(q)=-0.011q+37.4 To find: The consumer surplus corresponding to…

Q: (where Determine the point elasticity of demand of the demand function p k > 0).

A: Given, Demand function p= k/x where k>0.

Q: Suppose that the price p (in dollars) of a product is given by the demand function p =  18,000 − 60x…

A: Given query is to find the rate of change of price.

Q: If consumption is $7 billion when disposable income is $0, and if the marginal propensity to consume…

A: It is given that the consumption is $7 billion when disposable income is $0 and marginal propensity…

Q: The demand function for a certain product is determined by the fact that the product of the price…

A: We have, the product of the price and the quantity demanded equals 8000. Let us consider that, price…

Q: When a certain product is sold for p dollars per item, consumers will demand D(p)= 12,00p^-1 items…

A: Given, D(p)= 1200p-1 items/week p(t)= 0.5t²+6 dollars/item

Q: Suppose that a price-demand function is given by P(x)=100+10x−4x2. Calculate the marginal revenue…

A: Calculation:The price demand function is P(x) = 100+10x – 4 x^2.In order to calculate the marginal…

Q: Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.002x³ + 0.07x + 15x…

A: According to question given that Monthly cost of producing x chairs is…

Q: Suppose that the marginal propensity to save is   dS/dy = 0.24     (in billions of dollars) and…

A: Given that :dSdy=0.24 S(0)=$8.5 billion

Q: You run a small business that makes and sells widgets. Assume your daily rent and salaries total…

A:

Q: Assume that the situation can be expressed as a linear cost function.  Marginal cost is $25; 190…

A: GIVEN: Marginal cost = $25

Q: Suppose that the price p​ (in dollars) and the weekly sales x​ (in thousands of​ units) of a certain…

A:

Q: Suppose that the direct demand and direct supply functions are x = √200 - p and x = √p - 38,…

A:

Q: 5. Suppose that the marginal propensity to save is as TAVA (in billions of dollars) 3y+7 0.2- dy and…

A: Suppose that the marginal propensity to save is  ds/dy = 0.2 -1/√(3y+7) and that consumption is $6…

Q: A manufacturer has determined that m employees will produce a total of q units of product per day,…

A: the marginal-revenue product is given by dR/dm where R is the revenue. Using the chain rule of…

Q: If a demand curve is given by y = 50 −.02x  where x is the price in dollars, and y is the sales of…

A: Given demand curve is  y=50-0.02x where x is the price in dollars, and y is the sales of Really Big…

Q: Suppose that a price p and demand x are related through the price-demand equation x + 400p = 8, 000.…

A:

Q: if demand curve is p=500-4q. What is the value of marginal revenue when q=20

A:

Q: suppose that the price p(in dollars) and the weekly sales x (in thousands of dollars) of a certain…

A: Given query is to find rate of change of sales.

Q: Suppose the demand function for a product is given by the function: D(q) - 0.015q + 34.5 Find the…

A:

Q: If consumption is $5 billion when disposable income is $o, and if the marginal propensity to consume…

A:

Q: Suppose that the marginal propensity to consume is dc - 0.9 - e-2y (in billions of dollars) and that…

A:

Q: Suppose that the marginal propensity to save is ds = 0.24 dy (in billions of dollars) and that…

A:

Q: Suppose the demand function for a product is given by the function: D(q) - 0.015q + 34.5 Find the…

A:

Q: A manufacturer of a new patented product has found that he can sell 70 units a week to the customer…

A: Given problem is : A manufacturer of a new patented product has found that he can sell 70 units a…

Q: 2 9. For the cost function C(x)= 500x+.01x+400 a) find the average cost function and find the demand…

A: Cost function C(x) = 500x + 0.01x2 + 400   Average cost function Ax = Total cost functionNumber of…

Q: Suppose that the marginal propensity to consume is dc = 0.3 - e dy -0.5y (in billions of dollars)…

A: We will use concept of simple integration.

Q: When the admission price for a baseball game was $18 per ticket, 36,000 tickets were sold. When the…

A: Given- When the admission price for a baseball game was $18 per ticket, 36,000 tickets were sold.…

Q: Suppose that the marginal propensity to save is ds In(y + 1) = 0.96 – dy (in billions of dollars) y…

A:

Q: Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.002x + 0.07x + 19x +…

A: The given function is Cx=0.002x3+0.07x2+19x+700. d) The actual additional monthly cost of increasing…

Q: Find expressions for marginal revenue in the case when the demand equation is given by 1000 (a) P=…

A: (a).   The demand equation is: P=100-2Q where Q is the quantity of the product and P is the price…

Q: currently 40 chairs are produced monthly.   ​a) What is the current monthly​ cost? ​b) What is the…

A: Cost function

Q: Suppose that a price p and demand x are related through the price-demand equation x+400p=8,000.…

A: To work out the formula for the elasticity of demand at price p

Q: Suppose the demand for a product is given by 2p3q = 500,000p2 where p is price in dollars and q is…

A:

Q: If the demand curve for a particular commodity is p=0.09x+51 and the total cost function…

A:

Q: Suppose that the demand function for Brand X is P = 360 - 50Qd. Show whether going from 3 to 4 units…

A:

Q: Suppose a firm faces an inverse demand function given by P = a - BQ, where a, B > 0. Find the levecl…

A:

Q: supposed that a price-demand funtion P(x)=500-15x calculate marginal revenue function when x=10

A:

Q: Suppose the demand function for a product is given by the function: D(q) = – 0.013q + 55.9 Find the…

A:

Q: Find the consumer surplus for the demand curve P = 420 – 10q when g * = 20 items are sold at the…

A:

Q: Suppose that the demand function for a certain product isq = 400 - 4p(a) Enter the equation for…

A: Given:The demand function is q = 400-4p.

Q: Suppose that the marginal propensity to save is ds 0.20 (in billions of dollars) dy and that…

A: Consider the following: dsdy=0.20C=$5.35 billionDisposable income=$0Find National consumption…

Q: Suppose that the marginal propensity to consume is dc = 0.07 + dy In(y + 1) (in trillions of…

A:

Q: Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain…

A: Given demand equation, 4p³+x²= 4100 x=10 p=10 dp/dt=- $ .20/week Differentiating w.r.t to t we have,…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.