Let the inverse demand for a particular product be given by P=250-Q. The product
ID: 1120252 • Letter: L
Question
Let the inverse demand for a particular product be given by P=250-Q. The product if offered by two Cournot firms, each of which has a current marginal cost of $100. Both firms can invest a sum K to establish a research facility to develop a new process with lower marginal costs. The probability of success is p.
a. Assume that the new process is expected to have marginal costs of $70. Derive a relationship between K and p under which
i. neither firm establishes the research facility; ii. only one firm establishes a research facility; iii. both firms establish a research facility.
b. Can there be "too much" R&D? Illustrate your answers in a diagram with p on one axis and K on the other.
c. Now assume the marginal costs of the new process are expected to be $40. How does this affect your answers to question (a)?
1 Let the inverse demand for a particular product be given by P=250-Q. The product is offered by two Cournot firms each of which has a current marginal cost of $100. Both firms can invest a sum K to establish a research facility to develop a new process with lower marginal costs. The probability of success is . Assume that the new process is expected to have marginal costs of $70. Derive a relationship between K and a. under which i. neither firm establishes the ii. only one firm establishes a ii. both firms establish a research research facility: research facility facility b. Can there be too much R&D;? Illus- trate your answers in a diagram with on one axis and K on the other. Now assume that the marginal costs of the new process are expected to be $40. How does this affect your answers to c. I(a)?Explanation / Answer
Given is the inverse DD function; P=250-Q
Under Cournot model, the firms produce outputs q1 and q2 respectively. So, the DD function becomes P=250-q1-q2
Let Total revenue be symbolised by TR. so TR1=Pq1=(250-q1-q2)q1=250q1-q1^2-q1q2 and TR2=(250-q1-q2)q2=250q2-q1q2-q2^2
Marginal Revenue is denoted by MR. So, MR1=dTR1/dq1=250-2q1 and MR2=dTR2/dq2=250-2q2
When Marginal cost MC=100 equilibrium is MR1=MC and MR2=MC. That is 250-2q1=100, i.e. 2q1=150ie q1=75. and similarly q2=75
So the total cost =100q1+100q2+2K when each firm installs the research facility and MC1=MC2=70. Equilibrium q1*=q2*=90
TC=9000+9000+2K, i.e TC=18000+2K. When only one firm establishes the research facility TC=18000+K and when none installs the research facility TC=18000
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