(a) Competitive demand is the demand for commodities that can be used interchangeably. An increase in the demand for one will lead to a decrease in the demand for its substitute. Joint demand on the other hand is the demand for commodities that are used together to satisfy a want. An increase in the demand for one will lead to an increase in the demand for the other.

(b) i. From the diagram above (figure 1), an increase in the price of the complement of commodity R from P\(_{1}\) to P\(_{2}\) has resulted in a fall in quantity demanded from Q\(_{1}\) to Q\(_{}\). Demand for commodity R shifted from D\(_{1}\) to D\(_{2}\) and the equilibrium price fell from P\(_{1}\) to P\(_{2}\) and quantity from Q\(_{1}\) to Q\(_{2}\)

ii. An increase in the price of a substitute of Commodity R will result in a fall of its quantity demanded from Q\(_{1}\) to Q\(_{2}\). (in figure 3). As a result of this, demand for commodity R will increase, Shown by the demand curve shifting from D\(_{1}\)D\(_{1}\) to D\(_{2}\)D\(_{2}\) in figure 4. The equilibrium price will increase from P\(_{1}\) to P\(_{2}\) and equilibrium quantity from Q\(_{1}\) to Q\(_{2}\).
iii. The imposition of an indirect tax on commodity R will result in a shift of the supply curve from S\(_{1}\)S\(_{1}\) to S\(_{2}\)S\(_{2}\) in figure 5. with demand unchanged, the equilibrium price will increase from P\(_{1}\) to P\(_{1}\) but the equilibrium quantity will fall from Q\(_{1}\) to Q\(_{2}\).