Question

The following economic functions have been derived by the Finance Manager

Answer 1

The supply curve in the question is Qa = 3P2– 12 while the demand curve is Qx = 24 – P2.

a. How to ascertain the supply curve

To know the supply curve we have to be able to make a distinction of the direction of the signs used in the functions.

Supply curves are known to be positive because they are an increasing function that is due to prices. For demand function they are negative because they are a decreasing function.

In 3P2 – 12. the coefficient is positive when we take the first derivative. This gives us 6p= +6

For the demand curve, when we do this we would have -2p. that is -2 hence this is the demand curve.

2. Equilibrium.

At equilibrium we have Qa = Qd

hence  3P² – 12p= 24 – P²

From here we are to take like terms

3P² – 12p= 24 – P²

3P² +  P² - 12p - 24 = 0

4p² - 12p - 24 = 0

The solution to the quadratic equation using the quadratic equation calculator is x=4.37228 and x=−1.37228

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