Project 8 - Speech or Presentation Example

These parameters generate secondary parameters such as total cost, total revenue, average cost, and marginal revenue. All of them are interrelated. This assignment studies the interrelationship of these parameters using two equations: inverse demand and average cost. The inverse demand equation is represented by p = 800 – q and the average cost equation is expressed by c = q + 100 + 500/ q. The following sections present the interdependency of the above-mentioned primary and secondary parameters of the price and demand relationship.

The inverse demand equation is p = -q + 800. Therefore, the demand equation is q = - p + 800. This equation is coded in the Mathematica program to draw the 2D plot of the demand curve. The plot is drawn on the q-p plane; where q is independent variable quantity and p is the dependent variable demand. The plot is shown in Figure 2. Given Inverse demand function is p= -q + 800; therefore, Demand function is q = -p + 800. The formula for the calculation of Elasticity of demand is E = = *d(-q+800)/dq.

This formula is coded in the Mathematica , which are shown below. The demand elasticity for price, p =1 is E = -1/799. Since E < 1, demand is inelastic. Given average cost function, AC = q + 100 + 500 / q. For total quantity q, the total cost function is TC = (q+100+500/q)*q= q2 + 100q + 500. Marginal cost, MC is the tangent to TC function, which is expressed as The MC function will be expressed through q variable. The solution is MC = TC’[1]. The solution is coded in Mathematica, which are shown below.

We use the 3D profit function, f(π3D) = pq - q2 -100 q - 500. In this equation, p and q are independent variables. At the same time, for a given value of p there is a specific value of q. We find the values of q for p using p = - q + 800 equation. We assign p from 1 to 10 with interval 1. The 3D function and their arguments are coded in Mathematica. We have included a table of π3D = f (p, q)