Projects List
Project #1:
Parts I, II & III: The demand function for a product is p=10-0.1q and the average cost function is c ̅=0.4q+10+ 80/q , where p= price, and q=quantity demand.
Part IV:
f(x,y)= 2x+3y
g(x,y)=x^2+y^2=100
Project #2:
Parts I, II & III: The demand function is p=5-0.1q and the average cost function is
c ̅=0.1 q+1+150/q.
Part IV:
f(x,y)= 3x+4y
g(x,y)=x^2+y^2=100
Project #3:
Parts I, II & III: The demand function for product is p=-2q+100 and the average cost for producing q units is c ̅=6q-6+100/q , where p= price, and q= quantity demand.
Part IV:
f(x,y)= 4x-3y
g(x,y)=x^2+y^2=100
Project # 4:
Parts I, II & III: The demand function for product is p=-4q+400 and the average cost for producing q units is c ̅=37q+40+500/q , where p= price, and q= quantity demand.
Part IV:
f(x,y)= 2x+3y
g(x,y)=x^2+y^2=100
Project # 5:
Parts I, II & III: Suppose that the cost function for a product is given by C(q)=q^2+8q+10. The demand function for product is q=-4p+300.
Part IV:
f(x,y)= x+2y
g(x,y)=x^2+y^2=100
Project #6:
Parts I, II & III: Suppose that the cost of producing q appliances is C(q)=500-4q+q^2 and the demand function is given by p=14-2 q.
Part IV:
f(x,y)= 2x+y
g(x,y)=x^2+y^2=100
Project #7:
Parts I, II & III: Suppose that the dollar cost of producing q appliances is C(q)=15000-2 q+0.25q^2 and the demand function is given by q=40-1/3 p
Part IV:
f(x,y)= 4x+3y
g(x,y)=x^2+y^2=120
Project #8:
Parts I, II & III: The demand function for a monopolist’s product is q=300-1/2 p and the average cost per unit for producing q units is c ̅=19q-150+ 1200/q , where p= price, and q= quantity demand.
Part IV:
f(x,y)= 4x-3y
g(x,y)=x^2+y^2=60
Project #9:
Parts I, II & III: The demand function for a monopolist’s product is p(q)=1300-7q and the average cost per unit for producing q units is c ̅=0.004q^2-1.6 q+100+ 5000/q , where p= price, and q= quantity demand.
Part IV:
f(x,y)= 4x-y
g(x,y)=x^2+y^2=120
Project #10:
Parts I, II & III: The demand function for a monopolist’s product is p(q)=200-0.005q and the total cost for producing q units is c=20000+100q-0.03q^2+ 5/3 〖10〗^(-4) q^3 , where p= price, and q= quantity demand.
Part IV:
f(x,y)= 2x+y
g(x,y)=x^2-y^2=10
Questions
Use of MATLAB or Mathematica are recommended. Choose any of the projects and answer the question for your selected project at the end of this document. Provide the Matlab or Mathematica code for each question.
Part I
Develop the total revenue, total cost (if not given), and profit functions. Explain these functions in few sentences.
Develop a 2D plot for demand versus the price. What do you notice?
Develop a 2D plot for total cost versus the quantity; average cost versus the quantity; marginal cost versus the quantity; and marginal revenue versus quantity on the same graph. What do you notice?
Part II
Compute the point elasticity of demand.
Find the intervals where the demand is inelastic, elastic, and the price for which the demand is unit elastic.
Find the quantity that maximizes the total revenue and the corresponding price. Interpret your result.
Find the quantity that minimizes the average cost function and the corresponding price. Interpret your results.
What are the quantity and the price that maximize the profit? What is the maximum profit? Interpret your result.
Discuss the results of 6, 7 and 8.
Part III
In this part, we assume that the supply function is given by, p=8+q
Find the price and the quantity at the equilibrium.
Calculate the consumer surplus.
Calculate the producer surplus.
Part IV
If the function f(x,y)=⋯ is subject to the constrain〖 g(x,y)=⋯ 〗^
Use Lagrangian multipliers method to find the critical points of the function f(x,y).
Plot the function in the 3-D graph in MATLAB.
You can download the trial version of Matlab using the following link:
https://uk.mathworks.com/campaigns/products/trials.html?prodcode=ML
Sample Solution